Granul. Comput. (2016) 1:95–113 DOI 10.1007/s41066-015-0002-1

ORIGINAL PAPER

Interactive granular

1,2 3 1,4 Andrzej Skowron • Andrzej Jankowski • Soma Dutta

Received: 23 July 2015 / Accepted: 16 November 2015 / Published online: 5 January 2016 Ó The Author(s) 2015. This article is published with open access at Springerlink.com

Abstract Decision support in solving problems related to framework. The reasoning, which aims at controlling of complex systems requires relevant computation models for computations, to achieve the required targets, is called an the agents as well as methods for reasoning on properties of adaptive judgement. This reasoning deals with granules computations performed by agents. Agents are performing and computations over them. Adaptive judgement is more computations on complex objects [e.g., (behavioral) pat- than a mixture of reasoning based on deduction, induction terns, classifiers, clusters, structural objects, sets of rules, and abduction. Due to the uncertainty the agents generally aggregation operations, (approximate) reasoning schemes]. cannot predict exactly the results of actions (or plans). In Granular Computing (GrC), all such constructed and/or Moreover, the approximations of the complex vague con- induced objects are called granules. To model interactive cepts initiating actions (or plans) are drifting with time. computations performed by agents, crucial for the complex Hence, adaptive strategies for evolving approximations of systems, we extend the existing GrC approach to Interac- concepts are needed. In particular, the adaptive judgement tive Granular Computing (IGrC) approach by introducing is very much needed in the efficiency management of complex granules (c-granules or granules, for short). Many granular computations, carried out by agents, for risk advanced tasks, concerning complex systems, may be assessment, risk treatment, and cost/benefit analysis. In the classified as control tasks performed by agents aiming at paper, we emphasize the role of the -based achieving the high-quality computational trajectories rela- methods in IGrC. The discussed approach is a step towards tive to the considered quality measures defined over the realization of the Wisdom Technology (WisTech) program, trajectories. Here, new challenges are to develop strategies and is developed over years, based on the work experience to control, predict, and bound the behavior of the system. on different real-life projects. We propose to investigate these challenges using the IGrC Keywords Rough set Á (Interactive) granular computing Á Interactive computation Á Adaptive judgement Á Efficiency & Andrzej Skowron management Risk management Cost/benefit analysis [email protected] Á Á Á Big data technology Á Cyber-physical system Á Wisdom Andrzej Jankowski web of things Ultra-large system [email protected] Á Soma Dutta [email protected] 1 Introduction 1 Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland GrC has emerged from many different disciplines and 2 Systems Research Institute, Polish Academy of Sciences, fields, including General Systems Theory, Hierarchy The- Newelska 6, 01-447 Warsaw, Poland ory, Social Networks, Artificial Intelligence (AI), Human 3 The Dziubanski Foundation of Knowledge Technology, Problem Solving, Learning, Programming, Theory of Nowogrodzka 31, 00-511 Warsaw, Poland Computation, and Information Processing (Yao 2008). In 4 Vistula University, Stoklosy 3, 02-787 Warsaw, Poland recent years, one can observe a growing interest in the area 123 96 Granul. Comput. (2016) 1:95–113 of GrC as a methodology for modeling and conducting that are drawn together by indiscernibility, similarity, and/ complex computations, in various domains of AI and or functionality among the objects (Zadeh 1997). Each of Information Technology (IT). In particular, GrC brings a the granules according to its structure and size, with a very natural methodology for problem solving in AI. certain level of granularity, may reflect a specific aspect of Complex systems are becoming more and more important the problem, or form a portion of the system’s domain. GrC for applications in IT. Ultra-Large-Scale (ULS) systems is considered to be an effective framework in the design (Cyber-physical and ultra-large-scale systems 2013) are and implementation of intelligent systems for various real- some among them. ULS systems are interdependent webs life applications. The systems based on GrC, e.g., for pat- consisting of software-intensive systems, people, policies, tern recognition, exploit the tolerance for imprecision, cultures, and economies. ULS are characterized to have uncertainty, approximate reasoning as well as partial truth properties such as: (i) decentralization, (ii) inherently of soft computing framework, and are capable of achieving conflicting, unpredictable, and diverse requirements, (iii) tractability, robustness, and close resemblance with continuous evolution and deployment, (iv) heterogeneous, human-like (natural) decision-making (Bargiela and Ped- inconsistent, and changing elements, (v) erosion of the rycz 2003; Pedrycz 2013; Pedrycz et al. 2008; Skowron people/system boundary, and (vi) routine failures (Cyber- et al. 2011). physical and ultra-large-scale systems 2013). Cyber-Phys- In GrC, computations are performed on granules of ical Systems (CPSs) (Lamnabhi-Lagarrigue et al. 2014) different structures, where granularity of information plays and/or systems based on Wisdom Web of Things (W2T) an important role. Information granules (infogranules, for (Zhong et al. 2013) can be treated as special cases of ULS. short) in GrC are widely discussed in the literature (Ped- It is predicted that applications based on the above-men- rycz et al. 2008). In particular, let us mention here the tioned systems will have enormous societal impact and rough granular computing approach based on the rough set economic benefit. However, there are many challenges approach, and its combination with other approaches to soft related to such systems. In this article, we claim that further computing, such as fuzzy sets. However, the issues related development of such systems should be based on the rel- to the interactions of infogranules with the physical world, evant computation models. and perception of interactions in the physical world by There are several important issues which should be means of infogranules are not well elaborated yet. Under- taken into account in developing such computation standing interactions is one of the critical issues of complex models. Among them some are as follows. (i) Computa- systems (Goldin et al. 2006). For example, the ULS are tions are performed on complex objects with very dif- autonomous or semiautonomous systems, and cannot be ferent structures, where the structures themselves are designed as closed systems that can operate in isolation; constructed and/or induced from data and domain rather, the interaction and potential interference among knowledge. (ii) Computations are performed in an open smart components, among CPSs, and among CPSs and world and they depend on the interactions of physical humans, are required to be modeled by coordinated, con- objects. (iii) Due to uncertainty, the properties and results trolled, and cooperative behavior of agents representing of interactions can be perceived by agents only partially. components of the system (Cyber-physical and ultra-large- (iv) Computations are realized in the societies of inter- scale systems 2013). acting agents including humans. (v) Agents are aiming at We extend the existing GrC approach to IGrC by achieving their tasks by controlling computations. (vi) introducing complex granules (c-granules, for short) Agents can control computations using adaptive judge- (Skowron et al. 2012; Jankowski et al. 2014) making it ment, in which all of deduction, induction and abduction possible to model interactive computations carried out by are used. agents and their teams in complex systems working in an We propose to base our approach on the relevant com- open-world environment. putation model of IGrC framework, proposed recently as Any agent operates on a local world of c-granules. The an extension of the GrC. The label Granular Computing agent aims at controlling computations performed on was suggested by T. Y. Lin in late 1990s. c-granules from this local world for achieving the target Granulation of information is inherent in human think- goals. In our approach, computations in systems based on ing and reasoning processes. It is often realized that pre- IGrC proceed through complex interactions among physi- cision is sometimes expensive and not very meaningful in cal objects. Some results of such interactions are perceived modeling and controlling complex systems. When a by agents with the help of c-granules. problem involves incomplete, uncertain, and vague infor- The discussed approach is a step towards one way of mation, it may be difficult to discern distinct objects, and realization of the WisTech program (Jankowski and one may find it convenient to consider granules for tackling Skowron 2007). The approach was developed over years of the problem of concern. Granules are composed of objects work on different real-life projects. 123 Granul. Comput. (2016) 1:95–113 97

This article is organized as follows. In Sect. 2,an [...] interaction is a critical issue in the understand- introduction to IGrC is presented. In particular, we ing of complex systems of any sorts, [...] it has present intuitions concerning the definition of c-gran- emerged in several well-established scientific areas ules. Interactive computations on c-granules realized by other than computer science, like biology, physics, agents are discussed in Sect. 3. Issues related to agent’s social and organizational sciences. control based on IGrC are outlined in Sect. 4.Section5 Interactive computations of an agent in IGrC (Jankowski is devoted to the issues related to decision support of and Skowron 2007; Jankowski et al. 2014; Skowron and users in solving problems using IGrC. This section Wasilewski 2011; Skowron et al. 2012) are realized on includes comments on problem specification in IGrC configurations of c-granules generated by the agent’s (Sect. 5.1). Next, some strategies for construction and control. Roughly speaking, the aim of any c-granule is to discovery of new relevant granules are presented link relevant infogranule(s) (Pedrycz et al. 2008) with a (Sect. 5.2). In particular, such strategies can be based collection (or a structure) of spatiotemporal physical on (i) operations of aggregation of information systems objects from the agent’s environment perceived through (called as operations of joining with constraints), (ii) the ‘‘windows’’ of the c-granule. Collections (or structures) inducing a hierarchy of satisfiability relations, (iii) self- of spatiotemporal physical objects perceived by the agent organization of agents, or (iv) communications and through such windows are called hunks (Heller 1990; dialogue among agents. The approach to efficiency Jankowski et al. 2014; Skowron et al. 2012). The info- analysis, in particular to risk management, in control- granules linked by the c-granule with a particular collection ling computations over granules in Big Data Technol- (or structure) of spatiotemporal physical objects represent ogy(BDT),isoutlinedinSect.5.6. properties of interactions of objects from this collection (or The role of reasoning based on adaptive judgement is structure). discussed in Sect. 6. Section 7 concludes the paper. Any c-granule is synthesized with three physical com- The paper summarizes as well as extends the work ponents, namely soft_suit, link_suit and hard_suit. developed by Jankowski et al. (2014), Skowron and Jan- The soft_suit component of a given c-granule consists of kowski (2015) and Skowron et al. (2012, 2015). configurations of the hunks representing properties of the activity environment of ag; e.g., present, past, and expected results of activities of ag, as well as expected results of 2 Complex granules some potential interactions, activated by the c-granule, are parts of the soft_suit. It is used to record the properties of Infogranules are widely discussed in the literature (see, hunks and their interactions perceived by the c-granule. e.g., Skowron and Stepaniuk 2004). They can be treated as The link_suit can be treated as a communication channel specifications of compound objects, which are defined in a (composed out of links) transmitting results of interactions hierarchical manner, together with descriptions regarding among accessible fragments of the activity environment of their implementations. Such granules are obtained as the ag, including also results of interactions among hunks in result of information granulation (Zadeh 2001): the soft_suite. Note that some weights may be assigned to the links reflecting the results of judgement by ag based on Information granulation can be viewed as a human the priorities relative to the current hierarchy of needs of way of achieving data compression and it plays a key ag. role in implementation of the strategy of divide-and- The hard_suit is composed out of configurations of conquer in human problem solving. hunks accessible by links from the link_suit. Infogranules belong to those concepts which play the The soft_suit encodes procedures for: (i) recording some main role in developing foundations of AI, , properties of interactions among hunks in the hard_suit, and text mining (Pedrycz et al. 2008). They grew up as which are transmitted to soft_suit using link_suit, and (ii) some generalizations from theory, rough set initiating relevant interactions in the hard_suit. We assume theory, and interval analysis (Pedrycz et al. 2008). In GrC, that the relevant pointers to the link_suit, hard_suit, and/or to deal with vague concepts, rough sets, fuzzy sets, and soft_suit are represented in the soft_suit (or agent’s con- interval analysis are used. However, the issues related to trol), and make it possible to identify these components, if the interactions of infogranules with the physical world, necessary. We also assume that the soft_suit may represent and their relationship for perceiving interactions in the the information about the expected results of the perceived physical world are not well elaborated yet (Goldin et al. interactions, which take place in the hard_suit. 2006). On the other hand, in Goldin et al. (2006), it is In Fig. 1, we present an illustrative c-granule at a mentioned that: moment t of the agent’s time. The results of perception are

123 98 Granul. Comput. (2016) 1:95–113 stored in the soft_suit, and they include information about parts of the hunk perceived at time t (e.g., a pair of pen- x3 guins, a piece of ice land, and a camera). The soft_suit is x2 linked using link_suit, which plays a role of transmitting channel for interactions among the perceived hunks in the t hard_suit. Figure 2 illustrates changes of ‘windows’ for 4 t3 t t tracking of a particular pair of penguins over time. 2 5 t t6 Interactions of the agent with the environment are 1 t7 realized using configurations of c-granules. Due to the interactions of c-granules with the environment (including the agent’s control) the actual configuration of c-granules x1 of an agent is evolving with local time of the agent. This leads to the changes of the existing configuration of c-granules by • extending it to new c-granules selected by the agent’s control for perceiving new interactions (also stimulated Fig. 2 Links to a (spatiotemporal) hunk specified by the agent control using ‘‘windows’’ (see boxes in this figure), pointing to different by c-granules), fragments of the physical world (portions of matter) with the space • extending it to new c-granules for encoding the results coordinates x1; x2; x3 and the time coordinate t. Perception is realized of the perceived interactions, in different moments (or periods) of time t1; ...; t7 • deleting some c-granules from the current configura- tion, and • introducing other kinds of modifications of some parts • interpretation and judgement of importance of phe- of the configuration. nomena taking place in her/his activity environment; • judgement of phenomena from her/his environment (in In general, c-granules of ag support activities such as particular, causes and consequences of the phenomena) • improvement of techniques of representation according from the perspective of her/his hierarchy of needs; to her/his hierarchy of needs and perception of needs, • construction, initialization, realization, verification, as well as relations between them; adaptation, and termination of interaction plans;

Fig. 1 The c-granule intuition hard_suit

physical sensor, structure e.g., camera

link(s) creang a transming t 1 link_suit channel for More interacons between so _suit and hard_suit details

aribute recording a sensory measurement so _suit

perceived structure

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• communication, cooperation and competition of ag infogranules (interpreted as approximations of complex with other agents. vague concepts), relevant actions are undertaken by the Calculi of c-granules are defined starting from some ele- agent aiming to satisfy her/his needs. mentary c-granules, e.g., granules corresponding to reading An illustrative example of c-granule is presented in or storing measured values, simple sensory measurements, Fig. 3, where (i) his are hunks corresponding to the ‘‘space and indiscernibility or similarity of classes. The agent’s windows’’ (i.e., windows in the spatiotemporal space control as well as the interactions with the environment, which are constant over the agent’s time in the example) of make it possible to generate new c-granules from the c-granules in the network, (ii) sis denote link_suits for already defined ones. The hard_suits, link_suits, and transmitting interactions from his in the environment ENV 0 soft_suits of more compound c-granules are defined using to soft_suits of c-granules in the network, (iii) S; S are trees the relevant networks over already defined c-granules. The representing hierarchical aggregations of c-granules start- networks are satisfying some constraints, which can be ing from some input c-granules to some output c-granules 0 interpreted as definitions of types of networks. The link_- grounded on hunks h; h . These two hunks are encoded, 0 suits of such more compound granules are responsible for respectively, by infogranules C; C (see Fig. 3) belonging 0 transmission of interactions between the hard_suits and to the agent’s private language, where C; C represent soft_suits represented by the corresponding networks. The approximations of complex vague concepts used for initi- results and/or properties of transmitted interactions are ation of actions aci. The states (in the context of the given 0 recorded in the soft_suits. c-granule g) of hunks h; h at a given slot (moment) t of the 0 We assume that for any agent there is a distinguished agent’s time are recorded as some properties of h; h , and family of her/his c-granules creating the private language they are the perceived results (at the agent’s time moment 0 of the agent (Jankowski et al. 2014; Skowron et al. 2012). t)ofh; h , respectively. The states are interpreted as satis- 0 Moreover, we assume that elements of the private language fiability degrees of C; C . In this way, the perception of the can be encoded by infogranules. current situations in the environment ENV are represented. We also assume that information about states of some of The c-granules representing actions aci are initiated on the 0 the physical beings from the soft_suit can be decoded using basis of the satisfiability degrees of C; C representing the expressions from the private language of the agent. For currently perceived situation in the environment ENV. example, these can be propositional formulas over The process of perceiving the current situation is real- descriptors (Pawlak 1991; Pawlak and Skowron 2007)or ized first by transmitting interactions from hunks his cor- expressions from a (simplified) fragment of natural lan- responding to the ‘‘space windows’’ through the links sis, 0 0 guage (Zadeh 1979, 2001). Moreover, in the soft_suit of a and then through link_suits in S; S up to hunks h; h used to c-granule the interactions, which are perceived in the represent the perceived current situation. hard_suit through the transmitting channels from the link_suit, are recorded. This is typical for sensory mea- C surement. On the other hand, a c-granule may cause some interactions in its hard_suit by transmitting through its h link_suit some interactions from the soft_suit. However, S ac2 the c-granule may perceive the results (or properties) of ac1 such interactions in the hard_suit, only using the soft_suit. s This is done on the basis of the results (or properties) of s1 2 these caused interactions in the hard_suit, which are h2 ENV transmitted through the link_suit to the soft_suit. These h1 results (or properties) may be different from the predicted h4 ones, which can be stored a priori in the soft_suit. This is h3 typical for performing actions initiated by c-granules. s4 One should note that the process of distinguishing (or s3 ac discovering) the relevant family of c-granules creating the ac3 4 internal language is a very complex process. The relevant S’ infogranules are discovered in hierarchical aggregation of h’ infogranules considered in relevant contexts. In general, C’ such infogranules are called semiotic c-granules. Info- granules are used for constructing the target infogranules. Fig. 3 An example of c-granule g defined as a network (configura- On the basis of satisfiability (to a degree) of such target tion) of other c-granules

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These interactions lead to changes of states of h; h0. knowledge (e.g., ontology, rules for using language, These changes are encoded by changes of degrees of sat- history, applicable laws), selection of relevant knowl- 0 isfiability of C; C . The c-granules for actions acis are edge for supporting solutions of prioritized tasks/ responsible for initiating interactions in ‘‘space windows’’ actions; his corresponding to actions acis. The results of the mod- • ADAPTIVE PLANNING—problems identification and ified interactions caused by actions are transmitted through specification, tasks/ actions prioritization (based on the network to h; h0, which consequently leads to modifi- constrains specification), planning adaptation/change cation of their states. control, especially change of paradigms for dealing The discussed c-granules may represent complex with vague complex concepts and classifier objects. In particular, agents and their societies can be construction; treated as c-granules too. An example of c-granule repre- • EXPERIMENTS—improvement of acceptance criteria senting a team of agents is presented in Fig. 4, where some computation for satisfiability degrees of vague complex guidelines for implementation of AI projects in the form of concepts relevant to application requirements, scenario a cooperation scheme of different agents responsible for of testing experiments, preparation and execution relevant cooperation areas are illustrated. In the figure the experiments, results collecting and assessment; following members with exemplary competence areas are • CLASSIFIERS and OPTIMIZERS—selection and included: implementation of techniques for interactive learning of vague complex concepts, including adaptation and • DATA—data acquisition, assessment, cleansing, struc- use of inference and decision rules as arguments for or turing, management and governance; against decisions and conflict resolution—toward con- • PROBLEMS—identification, classification and struction of classifier societies (and/or intelligent prioritization, agents); optimizers for relevant classes of domain- • FEATURES—feature discovery, computation and specific problems (most of the classifiers, adaptation exploration up to maximally large and meaningful sets techniques and many other AI technologies depend on of potentially relevant features for important observed optimization techniques). and contextual phenomena; selection of potentially high quality and small subsets of features; This cooperation scheme may be treated as a higher • SENSORS and ACTUATORS—discovery, evolution level c-granule. We propose to model a complex system as and construction of sensors/actuators, adaptive control a society of agents. It is worthwhile mentioning that of sensor/actuator parameters, discovery of physical c-granules also create the basis for the construction of the world structures and phenomena; agent’s language of communication and the language of • DOMAIN KNOWLEDGE—acquisition, representa- evolution. tion, management and governance of domain An agent operates on a local world of c-granules. For achieving the target goals, the control of an agent, from the respective local world of the agent, aims at controlling

PROBLEMS computations performed on c-granules. Actions, also rep- idenficaon, classificaon & resented by c-granules, are used by the agent’s control in priorizaon exploration and/or exploitation of the environment on the ADAPTIVE EXPERIMENTS PLANNING way to achieve their targets. The c-granules are also used & PRODUCTION by agents for representing their perception about the INTERACTIONS interactions with the physical world. Due to the limited + ADAPTIVE JUDGEMENT DOMAIN ability of agent’s perception usually only a partial infor- KNOWLEDGE SENSORS & (with GRANULATION - in parcular AGGREGATION) mation about the interactions of the physical world may be ACTUATORS used by agent for control of perceived interacons) .... available to the agents. Hence, in particular the results of FEATURES the actions performed by agents cannot be predicted with certainty. For more details regarding IGrC based on c-granules the readers are referred to Jankowski et al. (2014) and Skowron et al. (2012). CLASSIFIERS & OPTIMIZERS DATA One of the key issues of the approach related to c-granules is a kind of integration between investigations Fig. 4 Cooperation scheme of an agent team responsible for relevant of physical and mental phenomena. This idea of integration competence area follows from the suggestions presented by many scientists.

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3 Interactive computations on c-granules realized environment, due to limitations of the available resources by agents (e.g., sensors), which are necessary for building agent’s perception strategies. Each agent’s configuration is composed out of c-granules. In Fig. 6, we illustrate how the abstract definition of The agent control initializes the initial configuration. In operation from soft_suit interacts with other suits of the Fig. 5 some possible components of an agent for interac- c-granule. It is necessary to distinguish two cases. In the tions are illustrated. Among them some are: case of soft_suit, the results of operation realized by the interactions of the hunks, available in the soft_suit itself, (i) control (C), should be consistent with the specifications encoded in the (ii) internal memory (M), link_suit. However, the result specified in the soft_suit can (iii) interactions realized by the control C between the be treated only as an estimation of the real one which may control granule and memory granule by means of be different due to the unpredictable interactions in the c-granules generated by control C for eliciting hard_suit. interactions Here, we would like to present a point of departure from (a) with the external environment (c-granules the Stephen Kleene’s proposal for (partial) recursive with parts: M, link l-2 (l-3) and hunk H-2 functions equivalent to the Turing model of computability. (H-3)) and Kleene’s definition is based on distinguishing some ele- (b) with internal parts of the agent other than mentary computable functions and some distinguished memory M (c-granule with parts: M, link operations under which the set of partial recursive func- l-1, and hunk H-1). tions is closed (Kleene 1936). In our case, the selection of what is an elementary The agent’s control generates new configurations of ‘‘computable’’ function depends on the agents ability to c-granules using, e.g., (i) formation of a c-granule repre- construct such a function in the physical world. For senting the configuration, (ii) initiation of interactions in example, one can consider the process of computing a the configuration, and (iii) recording of results of interac- value of a complex function using the quantum computing tions transmitted by links in the configuration. Note, that paradigm presented by Andrew Chi-Chih Yao, the Turing many activities in each of the steps may be realized con- award winner, during the panel discussion at the 2014 Web currently (or in parallel). Intelligence Congress (WIC 2014) (http://wic2014.mimuw. It is worthwhile mentioning that contrary to the existing edu.pl/) in Warsaw. He was discussing a gedanken exper- computation models realized by Turing machine, the iment for computing values of complex function results of interactions can be only predicted by the agent’s f(x) through the following steps: (i) grow a crystal C tai- control, but the results of this prediction can be in general lored to f and x, (ii) shine an optical wave on C, and (iii) different from the results of real interactions between agent from the diffraction pattern, figure out f(x). One can take and the environment due to uncertainty of the unpre- another point of view, and consider, e.g., real-valued sig- dictable environment. In particular, this may be implied by nals or videos as elementary functions. Another example is the uncertain information possessed by the agent about the related to the relational machine project by Ulam and Bednarek (1990), where the authors proposed to use some relations as elementary entities on which computations should be performed. They were trying to implement the idea using optical computing. The operations of aggregation of c-granules related to such complex objects are computationally admissible, if only we can realize them in the physical world. This sit- uation is illustrated in Fig. 6 concerning the computation of operation using c-granules embedded in the physical world. In Fig. 6 there are three distinguished parts of c- granule: soft_suit, link_suit, and hard_suit. ‘‘Computabil- ity’’ of the value ðG1; G2Þ (for given G1, G2), firstly requires (at the proper moments of the agent’s time) an access to the relevant physical configuration of objects (hard_suit) realized by interactions transmitted by links from the soft_suit to the relevant parts of the hard_suit into Fig. 5 Basic agent components for interactions which representations of arguments G1, G2 are encoded. 123 102 Granul. Comput. (2016) 1:95–113

Fig. 6 Illustration for so _suit infogranules aggregation implementation in G the physical world— 1 in so _suit ‘‘computability’’ of function corresponding G G to specificaon and G2 1 2 implementaon of operaon links for checking in the physical world of condions links for necessary for compung transmission of values of interacons making it possible to links for transmission of represent link_suitlink_suit interacons from the physical h) infogranules world (hunk making it possible to record in so _suit the G1 and G2 in the physical representaon G G world of 1 2 (using

hunks h1, h2 ) h 1 … h h2

hard_suit

Secondly, it needs to use links to initiate relevant interac- Natural Computing too. The agent’s observation to tions in the hard_suit responsible for computing the value understand such computations is dependent on the physical of the function . Finally, it needs encoding the value of world (see Deutsch et al. 2000, p. 268). on arguments G1; G2 by transmitting relevant interactions The agent hypotheses about the models of computations (using links) from the distinguished parts of the hard_suit can be verified only through interactions running in the to the soft_suit, and encoding the results of these interac- physical world. These models should be adaptive to tions properly in the soft_suit. Hence, the ‘‘computability’’ incorporate changes when deviations of the predicted tra- in our case depends on possibilities of perceiving and jectories of computations from the perceived real ones realizing in the physical world of relevant interactions. become significant. There are some other important differences between The issues discussed in this section raise a question interactive computations based on c-granules and Turing about the control over interactive granular computations. In computations which will be discussed in detail elsewhere. the following sections, we emphasize the importance of the Let us note here that the environment, over which com- risk management by the agent’s control. putations on c-granules run, is unknown to the agent. The agents, through interactions with the environment, are learning how to act effectively in it. After sufficient 4 Agent control based on IGrC and related tasks interaction agents may gain expertise, and this is not pro- vided a priori, but are extracted from the environment’s Agents realize their goals by performing actions. Hence, it behavior. is very important to discover some measures for evaluating The reader may compare the discussed model of inter- the correctness of a selection of a given action in a given active computations with ecorithms introduced by Valiant situation. For any action a, one can consider a complex (2013): vague concept Qa representing such a measure. For a particular situation s, the value of Q ðsÞ, is a c-granule Unlike most algorithms, they can run in environments a representing the degree to which Q ðsÞ is satisfied at s, i.e., unknown to the designer, and they learn by inter- a the correctness degree of the selection of the action a at s. acting with the environment how to act effectively in The c-granule Q ðsÞ consists of two main c-subgranules it. After sufficient interaction they will have expertise a representing arguments for and against the satisfiability of not provided by the designer, but extracted from the Q ðsÞ. These arguments are derived from the judgement environment. a based on the estimation that a potentially can be initiated at The point of view, that the interactive computing on the situation s with respect to the efficiency management complex granules needs to be based on the process of (Jankowski et al. 2014; Skowron et al. 2012). For example, interactions with the physical world, is important for in the risk assessment (ISO 31000 standard. http:// 123 Granul. Comput. (2016) 1:95–113 103 webstore.ansi.org/) the goal of the judgement is to identify mentioning that these games are evolving with time the main risks. On the basis of the risk degrees another (drifting with time) together with the data and knowledge judgement, called the risk treatment, is performed. Some about the approximated concepts as well as with the rele- modifications of performed actions, called controls (or new vant strategies for adaptation of games used by agents. controls), are considered against the existing (or possible) Hence, adaptive strategies are required for enabling agents vulnerabilities. These new controls could suggest of to control their behavior to achieve the targets. It is also to avoiding the risk, reducing the risk, removing the source of be noted that these strategies should be learned from the the risk, modifying consequences, changing probabilities, available uncertain data and domain knowledge. sharing the risks with other agents, retaining the risk or Let us summarize our considerations on the idea of even increasing the risk to pursue the opportunity (see discovery of games. Decision-making under uncertainty http://www.praxiom.com/iso-31000-terms.htm). involves large number of complex vague concepts. Among In a relevant fragment of natural language, one should them some are concepts related to identification of the judge the degrees of satisfiability of QaðsÞ for all relevant current situation, discovery of the relevant context relative actions. One should also judge conflict among the degrees to which one should consider the actual situation (by corresponding to different actions to select the best considering the past, the possible future, including risks, action(s) for execution at a given situation. costs or benefits), discovery of similarity measures of the One can consider the above-mentioned tasks of current situation (or plans) with the observed ones in the approximation of action guards as the task of complex past, discovery of relevant concepts for measuring the game discovery (see Fig. 7) from data and domain deviation degrees of the predicted situation with the real knowledge in cooperation with the domain experts. one. Moreover, for dealing with complex systems there is a The discovery process of complex games, in particular need for a language in which adaptive judgement over complex vague concepts which are embedded in them, concepts, relevant for these systems, could be performed. often is based on hierarchical learning supported by In particular, let us mention the need for adaptive judge- domain knowledge (see, e.g., Bazan 2008). An agent is ment for conflict resolution among the arguments for and interacting with the environment for discovering the con- against concerning the satisfiability of these concepts. The cepts and the cause–effect relationships relevant for the reader is also referred here to the paradigm of Computing complex games. These concepts and relationships are used with Words (CWW) (see, e.g., Zadeh 1996, 2001, 2012; by the agent to judge the results of interactions for efficient http://www.cs.berkeley.edu/*zadeh/presentations.html, initiation of relevant actions. It is also worthwhile and Sect. 6). The sentences made by Pearl (Pearl 2009) (see Sect. 5.6) and the paradigm of Perception-Based Computing (PBC) (e.g., Skowron and Wasilewski 2010; Zadeh 2001, 2012) are also relevant ideas to be referred to. so _suit One of the basic tasks of PBC is hierarchical learning of C1 C C 2 k complex vague concepts used for comprehending the per- h1 h2 hk ceived situations. Let us recall some sentences from S ac ac 1 ac k (Skowron and Wasilewski 2010) to explain that PBC is 1 S 2 S 2 … k related to IGrC: link_suit s1 s2 Perception is characterized by sensory measurements sk h h 2 and ability to apply them to reason about satisfiability 1 … h k of complex vague concepts used, e.g., as guards for ENVIRONMENT actions or invariants to be preserved by agents. Such hard_suit reasoning is often referred as adaptive judgement. Vague concepts can be approximated on the basis of Fig. 7 Complex game represented by a c-granule. This c-granule sensory attributes rather than defined exactly. consists of three other networks soft_suit, link_suit and hard_suit. The soft_suit consists of c-granules corresponding to hierarchical schemes Approximations usually need to be induced using S1; ...; Sk used for generating computational building blocks for hierarchical modeling. [...] Unfortunately, discovery approximation of complex vague concepts C1; ...; Ck representing of structures for hierarchical modeling is still a guards for initiation of actions (or plans) ac1; ...; ack. Judgement of challenge. On the other hand, it is often possible to satisfiability degrees of guards is used for initiation of actions. The acquire or approximate them from domain actions as well as links s1; ...; sk of hierarchical schemes to the corresponding hunks h1; ...; hk create link_suit. The hard_suit knowledge. consists of hunks h1; ...; hk: Agents are using actions to control interactions and, in consequence, the computations over granules are For real-life projects it is hardly possible to expect that progressing due to interactions the high-quality models of the discussed complex vague 123 104 Granul. Comput. (2016) 1:95–113 concepts can only be induced on the basis of automatic of problems to be solved). Let us note that scalability methods without acquiring the agents’ domain knowledge cannot be achieved without collective wisdom. Hence, the through cooperation with the domain experts. important area for the further development of the WisTech One natural direction is to construct dialogue systems program arises. different from the traditional data mining systems. In the In this section, a preliminary discussion on some main future, it will be then possible for users to formulate tasks, which should be supported by IGrC dealing with Big hypotheses, which the systems may verify interacting Data, is included. Among them, two are as follows. through a dialogue with the users. Such systems will allow 1. Filtering Big Data relative to the user’s view expressed us for more efficient discoveries. One can predict that such by the higher level primitives. systems will be widely used in other domains too. 2. Filtering Big Data relative to the user’s view about However, several challenges need to be resolved before specific problem (or class of problems). such systems get used widely. In particular, they are related to the ontology of (complex vague) concepts, and relations The first task is related to the relevant ontology develop- among them on which agents can base for problem solving. ment for the considered domain, as well as to the methods Moreover, one should consider a language in which of transferring it to systems for further use. Nowadays, adaptive judgement about satisfiability of these concepts there are many available tools for designing ontologies. and relations can be performed. A challenge is to transfer Methods for approximation of ontology have been also the ontology and the language to the system so that the developed (see, e.g., Bazan 2008; Nguyen et al. 2004) system becomes able to perform the necessary judgements making it possible to transfer ontology approximation to with satisfactory quality. the systems. Then, the system may use approximated In the study by Skowron and Jankowski (2015) and concepts and relations for generating new granules (e.g., Skowron et al. (2015), a discussion illustrating how rich new features or patterns) relevant for the approximation of such ontology can be, and how complex tasks are to be complex vague concepts. However, further work is needed solved using judgement is presented. Agents are perceiving for making these methods scalable for Big Data and a part of the open physical world, and they are interacting domain knowledge. with the perceived world. Concept and relations postulated In the following sections, we give some comments on in the study by Skowron and Jankowski (2015) and the issues related to the second task. Skowron et al. (2015) create the key ontological basis for WisTech (Jankowski and Skowron 2007). There are sev- 5.1 Problem specification by users eral groups of postulates. Some of them are related to the physical character of the agent, c-granules and interaction In this section, we discuss issues related to the specification models, while the others concern the efficiency manage- of problems, which may be faced by users for developing ment of judgements and the realization of the prioritized systems based on IGrC and Big Data. needs of the agent. The postulates are specifying some Let us consider the following challenge mentioned in basic concepts which are important for interactive com- Jagadish et al. (2014): putations on complex granules realized by agents for If users are to compose and build complex analytical achieving their goals. It is worthwhile mentioning that in pipelines over Big Data, it is essential they have (Skowron and Jankowski 2015; Skowron et al. 2015) only appropriate high-level primitives to specify their a general preliminary framework for applications in real- needs. life (intelligent) systems was formulated. There is a need for further work to make this specification more detailed Let us observe that the above-mentioned high-level and precise. primitives are often complex vague concepts, which are semantically ‘‘far away’’ from the raw data. Hence, to make such concepts available by the system it is necessary 5 IGrC and problem solving to develop methods for constructing (inducing) high-qual- ity classifiers for such concepts. The problem of specifi- One of the important challenges for the IGrC development cation, given by an user, is defined over such concepts. is to get scalable methods for data analytics (Jagadish et al. The user’s task may be to deliver the relevant granules 2014) including (i) scalable techniques for data manage- representing complex objects, satisfying the specification ment, relative to different classes of problems from dif- to a satisfactory degree (Polkowski and Skowron 2001). ferent domains, as well as (ii) efficient hybridization and Such granules are discovered and/or constructed using the integration of relevant techniques relative to the domain of hierarchical approach, where relevant strategies are to applications (expressed, e.g., by specification of the class search for relevant granules through granulation and 123 Granul. Comput. (2016) 1:95–113 105 degranulation processes. The delivered granules may be In the next section, we present some approaches which treated as computational building blocks for approximation appear to be very useful in searching for relevant calculi of of complex vague concepts representing the user’s speci- granules and particular granules from the families of fication. These approximations represent how the system is granules defined by these calculi. comprehending the user’s specification. We have already justified that the process of inducing such approximations 5.2 Construction and discovery of relevant granules is challenging. It is also worthwhile mentioning that approximations of In GrC, we create calculi of granules by specifying ele- concepts (such as concepts related to comprehending the mentary granules (e.g., indiscernibility or similarity clas- user higher level primitives or some expressions over them ses) and some operations constructing new granules from describing the situation and/or user needs) related to per- the already defined ones (Skowron and Stepaniuk 2004). In ception are induced by the system with the help of actions. this section, we briefly outline some of the approaches for For example, in the context of reasoning about changes new granule generation. For a given problem, one should of situation, one should take into account that the predicted discover a relevant calculi of granules, and deliver a actions or/and plans may depend not only on the changes of method of searching for relevant granules (in a selected past situations but also on the performed actions (or plans) calculi) which could be used as computational building in the past. This is strongly related to the idea of perception blocks for approximation of vague concepts used in the pointed out in Noe¨ (2004): problem specification. These vague concepts may represent guards of actions or plans performed by an agent. The The main idea of this book is that perceiving is a way actions are initiated on the basis of the judgement of sat- of acting. It is something we do. Think of a blind isfiability degrees of these guards in a given situation. person tap-tapping his or her way around a cluttered We start from granule aggregation defined by join space, perceiving that space by touch, not all at once, operations with the constraints over information systems but through time, by skillful probing and movement. (Skowron and Stepaniuk 2005). This approach allows us to This is or ought to be, our paradigm of what per- generate new infogranules of different types. Some of these ceiving is. infogranules are giving rise to new information systems. On the basis of the partial understanding of the user’s These systems can be used for generation of new info- specification, the system may deliver some proposals for granules such as indiscernibility or similarity classes of solutions. Next, the user may add some comments on them, granules of a given type, new attributes or features, clas- which in turn may help in improving or reconstructing the sifiers, clusters, and other patterns. In the case of c-granules delivered granules. The system should be able to ‘‘under- methods for aggregation of c-granules can be obtained in stand’’ these comments and search for the granules more an analogous way. However, discovery of relevant aggre- relevant to the user’s specification. A continuation of such gations becomes harder. We also explain how aggregations a dialogue between user and the system should lead to a of granules can be used in modeling self-organization satisfactory solution corresponding to the user’s require- process of agents. Through self-organization, new kinds of ments. Moreover, the whole ‘‘dialogue trajectory’’ should granules are generated. Then, we discuss how discovery of have an acceptable quality. The acceptability criterion a relevant hierarchy of the basic logical tools, namely could depend on the consumption of time in a dialogue for satisfiability relations, can be used for new granule gen- reaching a satisfactory solution. This means that the system eration. We also discuss interaction of granules realized should control the schemes of computation for achieving through dialogues of agents. Such interactions are leading the target goal. towards generation of new granules relevant for agents. One can treat the above-discussed case of problems as a Important classes of granules are related to private and special case of checking satisfiability of complex vague social languages of agents. Strategies for granule genera- concepts. These concepts can be interpreted as guards for tion by self-organization and communication of agents are initiation of actions or plans by the agent (see Sect. 4). In especially important for complex adaptive systems, where the discussed example related to Big Data, these actions the goal is to obtain relevant emergent behavioral patterns may represent users’ reactions on the solutions proposed by satisfying a given specification to a satisfactory degree the system. In this more general case, the granules con- (Desai 2005; Liu 2001). structed by the system are interpreted as the degrees (rep- We also emphasize the role of risk management in resenting arguments for and against) of satisfiability of controlling computations performed by agents over complex vague concepts. Let us note that the system c-granules. Finally, we discuss a special kind of reasoning should be equipped with strategies for resolving conflicts called adaptive judgement used by the agent’s control for between these arguments for and against. reasoning about granules and computations over them. This 123 106 Granul. Comput. (2016) 1:95–113 reasoning is also based on constructions over relevant corresponding join operation with constraints specifies a granules. construction of R from R1; R2. One can ask if such a con- struction can be modeled using simple local interactions 5.2.1 Context, structural objects, and self-organization only. For example, such local interactions may concern dependencies between values of attributes from the group One of the important problems in hierarchical learning of of attributes defined by the control of neighboring agents, the approximations of complex vague concepts is the dis- i.e., they can be fixed by neighboring agents. Here, we covery of relevant contexts on different levels of hierar- assume that the values of control attributes lying in the chical learning. Contexts can be modeled by aggregation of neighborhood of the first agent are perceived by the other information (decision) systems based on the join operations agents. Searching for relevant contexts under simple con- with their respective constraints (Skowron and Stepaniuk straints can be feasible. However, one should consider that 2005) (see Fig. 8). Cartesian product of the universes of such simplified searching not always can give the relevant aggregated information systems is filtered by constraints. aggregated constraints. One can observe here an analogy Constraints are specifying the structure of objects on the with the 13th Hilbert problem: new hierarchical level obtained by aggregation. The Can every continuous function of 3 variables be structure is defined by relations over the vectors of attribute written as a composition of continuous functions of 2 values from the aggregated information systems. Con- variables? straints can also be treated as specification of types of objects in the aggregated information systems. For more and the result by Vitushkin from 1954: details, the readers are referred to (Skowron and Stepaniuk There are continuously differentiable functions of 3 2005). variables which are not the superposition of contin- In the discussed case, there are two groups of (condi- uously differentiable functions of 2 variables. tional) attributes in information (decision) systems. The values of attributes from the first group are fixed by the The discussed problem is related to the self-organization agent’s control while the values of attributes from the other process initiated from local interactions and leading to group are the results of a function of values of attributes global emergent patterns. from the first group and interactions with environments. As The issues of self-organization have been intensively an instance, let us consider that parameters of sensors or studied for years (e.g., Estep 2014; Pfeifer et al. 2007). actions, which need to be activated, belong to the first Methods based on self-organization are crucial for dealing group of attributes. Then the sensory measurements, based with Big Data, and further research is required in this on the values from the first group and interactions with regard. environments, constitute the values of the attributes of the Let us refer here once again to (Pfeifer et al. 2007) second group. (p.1088): Top-down decomposition strategies of specification [...] viewing an [...] agent [...] as a complex create such schemes with the help of which construction of dynamical system enables us to employ concepts such relevant patterns can be discovered. Let us consider an as self-organization and emergence rather than example of decomposition of information systems with the hierarchical top-down control. [...] autonomous type of objects characterized by relation R over tuples of agents display self-organization and emergence at attribute-value vectors into two information systems with multiple levels: at the level of induction of sensory object types characterized by relations R ; R . The 1 2 stimulation, movement generation, exploitation of morphological and material properties, and interac- tion between individual modules and entire agents. A We propose to use the top-down decompositions for W generation of decomposition schemes, along which dis- covery of agent’s self-organization may proceed (e.g., constraints aiming at discovery of relevant contexts or object struc- tures for the generation of relevant emergent patterns). A … Ak 1 These schemes are making the discovery process of self- organization feasible by bottom-up realization using the Fig. 8 Join with constraints W of information systems A1; ...; Ak to top-down decomposition schemes acquired from users. information system A. The constraints are used for filtering relevant tuples of objects from the Cartesian product of the object universes of However, one should also note that the decomposition A1; ...; Ak, e.g., those which are sufficiently close or similar schemes generated in the top-down decomposition create 123 Granul. Comput. (2016) 1:95–113 107 only hypotheses. Hence, searching for discovery of rele- remark made by Martin-Lo¨f(1984) about judgement pre- vant decompositions will require backtracking. Further sented in Fig. 10. development of methods for discovery of self-organization In the approach based on c-granules, the judgement for still requires much more work. Here, we would like to checking values of descriptors (or more compound for- mention only the important interactions in this learning mulas) pointed by links from simple c-granules is based on process of top-down decompositions with bottom-up self- interactions of some physical parts considered over time organization. and/or space (called hunks) and pointed by links of c-granules. The judgement for the more compound 5.2.2 Satisfiability and new granules c-granules is defined by a relevant family of procedures also realized by means of interactions with the physical Let us observe that the satisfiability relations in the IGrC parts. framework can be treated as tools for constructing new Let us explain the above claims in more detail. information granules. In fact, for a given satisfiability Let us assume that a given agent ag has at the her (his) relation, the semantics of formulas relative to this relation disposal a family of satisfiability relations is defined. In this way the candidates for new relevant fƒig ; ð1Þ information granules are obtained. We would like to i2I emphasize on this very important feature that the relevant where ƒi TokðiÞÂTypeðiÞ, TokðiÞ is a set of tokens and satisfiability relation for the considered problems, is not TypeðiÞ is a set of types (using the terminology from given but it should be induced (discovered) on the basis of Barwise and Seligman 1997). The indices of satisfiability a partial information encoded in the respective information relations are vectors of parameters related to time, space, (decision) systems. For real-life problems, it is often nec- spatiotemporal features of physical parts represented by essary to discover a hierarchy of satisfiability relations hunks, or actions (plans) to be realized in the physical before we obtain the relevant target level. Information world. granules constructed at different levels of this hierarchy finally lead to relevant ones for the approximation of complex vague concepts represented by complex granules context in a metalanguage expressed in natural language (see Fig. 9). proposion A is true over which judgement is Let us discuss some examples of c-granules constructed performed over a family of satisfiability relations being at the disposal of a given agent. This discussion has some roots in intu- Fig. 10 Judgement of truth in a metalanguage: ‘‘When we hold a itionism (see, e.g., Martin-Lo¨f 1984). Let us consider a proposition to be true, then we make a judgement’’ (Martin-Lo¨f 1984)

Fig. 9 Interactive hierarchical arribute a over structural objects structures [gray arrows show links transming interactions between interacons with hierarchical hierarchical levels and the the environment … … environment, arrows at a … levels over hierarchical levels point from which information (decision) systems sasfiability representing partial structural object relaons are specifications of satisfiability construcon using induced relations to induced from them … theories consisting of rule sets] join with constraints … over objects from the … lower level and the … … … environment …

…

… … …

123 108 Granul. Comput. (2016) 1:95–113

In the discussed example of elementary c-granules, from the ontology discovered on lower levels of the hier- TokðiÞ is a set of hunks and, TypeðiÞ is a set of descriptors archy of satisfiability relations should make it possible to (elementary infogranules) (Pawlak and Skowron 2007), generate the relevant computational building blocks for respectively, pointed by the link represented by ƒi. The inducing on the next hierarchy levels, e.g., the model of procedure for computing the value of h ƒi a, where h is a similarity relation between the treatment plans (delivered hunk and a is an infogranule (e.g., descriptor or formula by medical expert, and predicted by the decision support constructed over descriptors), is based on the interaction of system) (Bazan 2008). Searching for relevant satisfiability a with the physical world represented by the hunk h. relations is related to adaptive judgement. The agent’s control can aggregate some simple c-gran- ules into more compound c-granules. For example, by 5.2.3 Comments on dialogues of agents in IGrC selecting some constraints on subsets of I it is possible to select relevant sets of simple c-granules generated by ƒi In this section, we present some preliminary comments on over these subsets, and consider them as new, more com- dialogues among agents. Dialogues of agents from a given pound c-granules. For example, constraints over values of team can lead to a common understanding of the problems descriptors pointed by links of elementary c-granules can of concern and help to get a cooperative problem solving be taken into account, and sets of descriptors selected by strategy. The issues related to reasoning based on dialogues such constraints can be used to create more compound are not trivial, especially when one would like to propose a c-granules. Values of new descriptors (pointed by links of treatment incorporating the possibility of combining dif- these more compound granules) are computed by new ferent dominating paradigms of reasoning in logic. This procedures. The computation process again is realized point of view was well expressed by Johan van Benthem in through interaction with the physical parts represented by Rahwan and Simari (2009) (see Foreword, p.viii): hunks, which are pointed by links of c-granules, included I see two main paradigms from Antiquity that come in the compound c-granule. Moreover, in a procedure for together in the modern study of argumentation: computing the values of more compound descriptors the Platos Dialogues as the paradigm of intelligent values of the descriptors included in the elementary interaction, and Euclids Elements as the model of c-granules (of the considered more compound c-granule) rigor. Of course, some people also think that formal are used. It is to be noted that this procedure is also realized mathematical proof is itself the ultimate ideal of in the physical world with the help of the relevant reasoning - but you may want to change your mind interactions. about reasonings peak experiences’ when you see top In hierarchical modeling aiming at inducing relevant mathematicians argue interactively ats a seminar. c-granules (e.g., for approximation of complex vague concepts), one can consider so far constructed c-granules as Dialogues enable the agents to (efficiently) search for tokens. For example, they can be used to define structured solutions. Very often a query, formulated in IGrC by an objects representing corresponding hunks, and using new agent, involves vague concepts from natural language; e.g., satisfiability relations (from a given family) they can be one can consider queries given by an user to a dialogue- linked to the relevant higher order descriptors together with based search engine. Agents are expecting to receive the appropriate procedures (realized by interactions of c-granules satisfying their specifications to some satisfac- hunks) for computing values of these descriptors. This tory degrees. The meaning of satisfiability to a degree approach generalizes hierarchical modeling developed for should be learned on the basis of dialogues among agents infogranules (see, e.g., Bazan 2008; Nguyen et al. 2004)in embedded in the systems based on IGrC. Satisfiability to a the context of hierarchical modeling of c-granules, which is degree gives some flexibility in searching for solutions. important for many real-life projects. The solutions do not need to be exact. This may make the We have assumed before that the agent ag is equipped process of searching for constructions of such c-granules with a family of satisfiability relations. In the framework of feasible. It is worthwhile mentioning that such construc- GrC, based on c-granules, satisfiability relations are tools tions should be robust relative to the deviations of for constructing new c-granules. In fact, for a given satis- components. fiability relation, the semantics of descriptors (and more Using dialogues, agents may try to recognize the compound formulas) relative to this relation can be defined. meaning of c-granules received from the other agents. They However, in real-life cases the situation is more com- can do this by learning approximations of received plicated. The agent ag should have strategies for discov- c-granules in their own languages. A given agent may ering new relevant satisfiability relations on the way of acquire the description of ontology of the concepts used by searching for target goals (solutions of problems). For another agent. However, usually a given agent can only example, the approximations of concepts and relations acquire an approximation of concept-ontology possessed 123 Granul. Comput. (2016) 1:95–113 109 by another agent. This idea of shared knowledge among management. Currently, the dominant terminology is agents may be very useful in solving problems by any determined by the standards of ISO 31K (ISO 31000 individual agent (see e.g., Bazan 2008; Nguyen et al. standard. http://webstore.ansi.org/). However, the logic of 2004). Let us note that the ontology approximation may inferences in risk management is dominated by the statis- also be used in efficient searching for relevant contexts of tical paradigms, especially by Bayesian data analysis ini- queries received by agents from other agents. tiated about 300 years ago by Bayes, and regression data One of the challenges for adaptive judgement, per- analysis initiated about 200 years ago by Legendre and formed by a given agent ag, is the task of learning the Gauss. They initiated many detailed methodologies specific approximation of derivations performed by another agent for different fields. A classic example is the risk manage- ag0, assuming that an approximated concept-ontology of ment methodology in the banking sector, based on the ag0 is already available to ag. The agent ag may approxi- recommendations of Basel II standards for mathematical mate, to a satisfactory degree, the derivations performed by models of risk management. The current dominant statis- ag0 with the help of the constructions of solutions delivered tical approach is not satisfactory because it does not give by ag0. effective tools for inferences about the vague concepts and relations between them. 5.3 Risk management by agents in IGrC A particularly important example of a vague relation in risk management is the relation of a cause–effect depen- In this section, we add some comments on risk manage- dencies between various events. It should be noted that the ment. Let us note that practical judgement is involved in concept of risk in ISO 31K is defined as the effect of efficient management (Jankowski et al. 2014; Skowron uncertainty on objectives. Thus, by definition, the vague- et al. 2012). ness is also an essential part of the risk concept. Risk may be understood as interaction (of agents) with A slightly modified version of sentences of Pearl (2009) uncertainty (of environment). Perception of risk is a sub- for risk management can be presented as follows: tradi- jective judgement, which people make about the severity tional statistical approach to risk management inference is and/or probability of a risk. This may vary from one person strong in devising ways of describing data and inferring to another. Any human endeavor carries some risk, but distributional parameters from sample. However, in prac- some are much riskier than the others (The Stanford tice risk management inference requires two additional Encyclopedia of Philosophy: http://plato.stanford.edu/ ingredients: archives/spr2014/entries/risk/). • a science-friendly language for articulating risk man- Since the very beginning, all human activities were done agement knowledge, and at risk of failure. We have seen the low quality of risk • a mathematical machinery for processing that knowl- management in areas such as finance, economics, and edge, combining it with data and drawing new risk many others in the recent years. In this regard, improve- management conclusions about a phenomenon. ment in the risk management is of a particular importance for the further development of complex systems. The As very accurately specified by the Turing test, adding both importance of risk management illustrates the following the above-mentioned components is an extremely difficult example from the financial sector. Many of financial risk task, and relates to the core of AI research. In the context of management experts consider Basel II rules (see http://en. our applications, the idea of Turing test boils down to the wikipedia.org/wiki/Basel_Committee_on_Banking_Super fact that on the basis of a ‘‘conversation’’ with a hidden risk vision) as a causal factor in the credit bubble prior to the management expert and a hidden machine one will not be 2007–2008 collapse. Namely, in Basel II one of the prin- able to distinguish who is the man and who is the machine. cipal factors of financial risk management was We propose to extend the statistical paradigm by adding the two above-discussed components for designing the outsourced to companies that were not subject to high-quality risk management systems based on IGrC. supervision, credit rating agencies. For the risk management based on IGrC one of the most Of course, now we do have a new ‘‘improved’’ version important task is to develop strategies for inducing of Basel II, called Basel III. However, according to an approximations of the vague complex concepts involved in OECD (see http://en.wikipedia.org/wiki/Basel_III) the the domain of concern of the risk management. Let us note medium-term impact of Basel III implementation on GDP that the approximations are providing methods for check- growth is negative and estimated in the range of À0:05% to ing their satisfiability (to a degree). A typical example of À0:15% per year (see also Slovik 2011). such vague concept is the statement of the form: ‘‘now we On the basis of experience from many areas, we have do have a very risky situation’’. Among such concepts, the now many valuable studies on different approaches to risk complex vague concepts representing the role of guards, on 123 110 Granul. Comput. (2016) 1:95–113 which the activation of actions performed by agents are conflict resolution, adaptation of measures based on the based, are of special importance. minimum description length principle), These vague complex concepts are represented by the • prediction of changes, agent’s hierarchy of needs. In the risk management, one • initiation of relevant actions or plans, should consider a variety of complex vague concepts and • discovery of relevant contexts, relations between them, as well as the reasoning schemes • adaptation of different sorts of strategies (e.g., for related to the bow tie diagram (Skowron et al. 2012). existing data models, quality measures over computa- tions realized by agents, objects structures, knowledge representation and interaction with knowledge bases, 6 Adaptive judgement ontology acquisition and approximation, hierarchy of needs, or for identifying problems to be solved The reasoning which is used to support problem solving, according to priority of needs), makes it possible to derive relevant c-granules, and control • learning the measures of inclusion between granules interactive computations over c-granules for achieving the from sources using different languages (e.g., the formal target goals, is called an adaptive judgement. language of the system and the user natural language) Adaptive judgement over interactive computations is a through dialogue, mixture of reasoning based on deduction, abduction, and • strategies for development and evolution of communi- induction. In particular, case-based reasoning, analogy- cation language among agents in distributed environ- based reasoning, reasoning from experience, reasoning ments, and based on observed changes in the environment, or rea- • strategies for efficiency management in distributed soning with application of meta-heuristics from natural computational systems. computing are used. One should note that judgment fig- Below we discuss some issues related to adaptive judge- ures in the explanation of behavior, in inference, and in ment in IGrC. experience. Hence, the theory of judgment has roots in In some cases judgement methods may be based on psychology, in logic, and in phenomenology (Martin formal languages, i.e., the expressions from such languages 2006). In particular, the meaning of practical judgement are used as labels (syntax) of granules. However, there are goes beyond typical tools for reasoning based on deduction also paradigms such as Computing With Words (CWW), or induction (Thiele 2010): due to Professor Lotfi Zadeh (Zadeh 1996, 2001, 2012), Practical judgement is not algebraic calculation. where labels of granules are words (i.e., words or expres- Prior to any deductive or inductive reckoning, the sions from a relevant fragment of natural language), and judge is involved in selecting objects and relation- computations are performed on words (http://www.cs.ber ships for attention and assessing their interactions. keley.edu/*zadeh/presentations.html). In IGrC it is nec- Identifying things of importance from a potentially essary to develop new methods extending the approaches endless pool of candidates, assessing their relative for approximating vague concepts expressed in natural significance, and evaluating their relationships is language, and for approximating reasoning on such con- well beyond the jurisdiction of reason. cepts. It is also important to note that information granu- lation plays a key role in implementation of the strategy of For example, a particular question for the agent’s con- divide-and-conquer in human problem solving (Zadeh trol concerns discovering strategies for models of dynamic 1979, 2001). Hence, it is important to develop methods changes of the agent’s attention. This may be related to which could perform approximate reasoning along such discovery of changes in a relevant context necessary for the decomposition schemes, delivered by the strategy of judgement. divide-and-conquer in human problem solving, and induce Let us note that the intuitive judgement and the rational the relevant granules as computational building blocks for judgement are distinguished as different kinds of constructing the solutions for the considered problems. judgement. In case of systems, based on IGrC, the users are often Among the tasks for adaptive judgement there are the specifying problems in fragments of a natural language following ones supporting reasoning towards, with the constraint, that their solutions will satisfy speci- • inducing relevant classifiers (e.g., searching for relevant fications to some satisfactory degrees. Hence, methods for approximation spaces, discovery of new features, approximation of domain ontology (i.e., ontology on which selection of relevant features (attributes), rule induc- a fragment is based) as well as approximations of con- tion, discovery of inclusion measures, strategies for structions representing solutions based on concepts from

123 Granul. Comput. (2016) 1:95–113 111 the domain ontology should be developed. The rough set inducing of ARSs are still under development. The systems approach in combination with other soft computing for problem solving are enriched not only by approxima- approaches is used for approximation of the vague con- tions of concepts and relations from ontologies but also by cepts (Bazan 2008). These approximations may help the ARSs. system to follow, in an approximate sense, the judgement We would like to stress that still much work should be schemes expressed in the relevant (for the considered done to develop approximate reasoning methods about problems) fragment of a natural language. It is worthwhile complex vague concepts for the progress of the develop- to emphasize here the importance of dialogues between ment of IGrC, in particular for the efficiency management users and system in the process of obtaining the relevant in systems based on IGrC. This idea was very well approximations. expressed by Leslie Valiant (see, e.g., http://en.wikipedia. Very often the problems related to systems based on org/wiki/Vagueness, http://people.seas.harvard.edu/*vali IGrC concern control tasks. Examples of control tasks ant/researchinterests.htm; Valiant 2013): may be found in different areas, such as the medical A fundamental question for artificial intelligence is to therapy support, management of large software projects, characterize the computational building blocks that algorithmic trading or control on unmanned vehicles, to are necessary for cognition. A specific challenge is to name a few. Such projects are typical for ULS. Any of build on the success of so as to such exemplary projects is supported by (large) data and cover broader issues in intelligence. [...] This domain knowledge distributed over computer networks requires, in particular a reconciliation between two and/or Internet. Moreover, interactions of agents with the contradictory characteristics – the apparent logical physical world, which are often unpredictable, are nature of reasoning and the statistical nature of unavoidable. Computations performed by agents are learning. aiming at constructing, learning, or discovering granules, which in turn makes it possible to understand the con- It should be noted that the approach based on IGrC is cerned situation (state) to a satisfactory degree. The rel- well suited for implementation. This was proved, e.g., in evant control of computations based on understanding of inducing c-granules [such as clusters, time windows or the situation is realized using approximations of complex their sequences, similarity neighborhoods, processes, clas- vague concepts playing the role of guards, responsible for sifiers (Skowron and Stepaniuk 2005), see also Sect. 5.4]in initiation of actions (or plans) by agents. In particular, hierarchical learning (see, e.g., Bazan 2008; http://www. different kinds of granules, discovered from data, are used mimuw.edu.pl/*bazan/roughice/?sLang=en). The induced for constructing these approximations. The main pro- c-granules are used as computational building blocks for cesses, namely granulation and degranulation, character- approximation of high-level specifications (often expressed ize, respectively, the synthesis and decomposition of in natural language) or complex games (see Sect. 4). On granules in the process of constructing relevant resultant different levels of hierarchy, c-granules are used to repre- granules. sent structural objects and also as features (attributes) over The efficiency management in controlling the compu- such objects (see Sect. 5.4). Also methods for discovery of tations in IGrC are of great importance for the successful c-granules in the form of approximate reasoning schemes behavior of individuals, groups or societies of agents. In were developed (see, e.g., Skowron and Stepaniuk 2004 particular, such efficiency management is important for and Sect. 6). It is worthwhile mentioning that there is a constructing systems based on large data for supporting need for developing methods for inducing complex net- users in problem solving. The efficiency management works of c-granules relevant for more complex tasks. For covers risk assessment, risk treatment, and cost/beneft example, actions or plans should be embedded into hier- analysis. The tasks related to this management are related archies of c-granules what leads to feedback loops in the to control tasks aiming at achieving the high-quality per- networks. Such networks of c-granules (which are also formance of (societies of) agents. One of the challenges in c-granules!) aim at preserving some invariants (over time) efficiency management is to develop methods and strate- of complex systems, e.g., representing the requirements for gies for adaptive judgement related to adaptive control of high security of the system. Further development of IGrC computations. The efficiency management in decision foundations will bring methods for inducing c-granules systems requires tools to discover, represent, and access being complex networks in which also physical objects approximate reasoning schemes (ARSs) (over domain (such as robots or different units) and humans exist. This is ontologies) representing the judgement schemes (Bazan very important for development of ULS systems, in par- 2008; Skowron and Stepaniuk 2004). ARSs are approxi- ticular for CPSs and W2T. This will help to deal with mating, in a sense, judgements expressed in relevant challenges for such systems (Lamnabhi-Lagarrigue et al. fragments of simplified natural language. Methods for 2014). 123 112 Granul. Comput. (2016) 1:95–113

7 Conclusions creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a The approach for modeling interactive computations based link to the Creative Commons license, and indicate if changes were on c-granules is presented, and its importance for the made. efficiency management of controlling interactive compu- tations over c-granules is outlined. It is worthwhile men- tioning that in modeling and/or discovering granules, tools References from different areas are used. Among these areas some are machine learning, data mining, multi-agent systems, com- Bargiela A, Pedrycz W (eds) (2003) Granular Computing: An Introduction. Kluwer Academic Publishers, Dordrecht plex adaptive systems, logic, cognitive science, neuro- Barwise J, Seligman J (1997) Information Flow: The Logic of science, and soft computing. IGrC is aiming at developing Distributed Systems. Cambridge University Press, Cambridge a unified methodology for modeling and controlling com- Bazan J (2008) Hierarchical classifiers for complex spatio-temporal putations over complex objects, called c-granules, as well concepts. In: Transactions on Rough Sets IX: Journal Subline. LNCS, vol 5390, pp 474–750 as for reasoning about such objects and computations over Cyber-physical and ultra-large scale systems (2013). http://resources. them. In particular, such a methodology is of great sei.cmu.edu/library/asset-view.cfm?assetid=85282 importance for ULS. Desai A (2005) Adaptive complex enterprises. Commun ACM The discussed concepts such as interactive computation 45:32–35 Deutsch D, Ekert A, Lupacchini R (2000) Machines, logic and and adaptive judgement are among the basic ingredients in quantum physics. Bull Symb Log 6:265–283 the field of WisTech. Let us mention here the WisTech Estep M (2014) Self-organizing natural intelligence: Issues of meta-equation: knowing, meaning, and complexity. Springer, Heidelberg Goldin D, Smolka S, Wegner P (eds) (2006) Interactive Computation: WISDOM ¼ INTERACTIONS the New Paradigm. Springer, Berlin þ ADAPTIVE JUDGEMENT ð2Þ Heller M (1990) The Ontology of Physical Objects. Four Dimensional Hunks of Matter. Cambridge Studies in Philosophy. Cambridge þ KNOWLEDGE: University Press, Cambridge, Jagadish H, Gehrke J, Labrinidis A, Papakonstantinou Y, Patel JM, The presented approach has a potential for being used for Ramakrishnan R, Shahabi C (2014) Big data and its technical developing computing models in different areas, such as challenges. Commun ACM 57:86–94 natural computing (e.g., computing models for meta- Jankowski A, Skowron A (2007) A WisTech paradigm for intelligent systems. In: Transactions on Rough Sets VI. LNCS, vol 4374. heuristics or computing models for complex processes in Springer, Heidelberg, pp 94–132 molecular biology), computing in distributed environments Jankowski A, Skowron A, Swiniarski RW (2014) Interactive complex under uncertainty realized by multi-agent systems (e.g., in granules. Fundamenta Informaticae 133:181–196 social computing), modeling of computations for feature Kleene SC (1936) General recursive functions of natural numbers. Mathematische Annalen 112:727–742 extraction (constructive induction) used for approximation Lamnabhi-Lagarrigue F, Di Benedetto MD, Schoitsch E (2014) of complex vague concepts, hierarchical learning, discov- Introduction to the special theme cyber-physical systems. Ercim ery of planning strategies or strategies for coalition for- News 94:6–7 mation by agents as well as for approximate reasoning Liu J (2001) Autonomous Agents and Multi-agent Systems: Explo- rations in Learning, Self-organization and Adaptive Computa- about interactive computations based on such computing tion. World Scientific Publishing, Singapore models. In our research, we plan to further develop the Martin WM (ed) Theories of Judgment. Psychology, Logic, foundations of interactive computations based on c-gran- Phenomenology. Cambridge University Press, New York (2006) ules. The approach will be used for the development of Martin-Lo¨f P (1984) Intuitionistic Type Theory (Notes by Giovanni Sambin of a series of lectures given in Padua, June 1980). models of computations and their analysis in Natural Bibliopolis, Napoli Computing (Rozenberg et al. 2012), W2Ts (Zhong et al. Nguyen SH, Bazan J, Skowron A, Nguyen HS (2004) Layered 2013), CPSs (Lamnabhi-Lagarrigue et al. 2014), and ULS learning for concept synthesis. In: Transactions on Rough Sets I: (Cyber-physical and ultra-large-scale systems 2013). Journal Subline. LNCS, vol 3100, pp 187–208 Noe¨ A (2004) Action in Perception. MIT Press, Cambridge Pawlak Z (1991) Rough Sets: Theoretical Aspects of Reasoning about Acknowledgments This work by Andrzej Skowron and Andrzej Data. System Theory, Knowledge Engineering and Problem Jankowski was partially supported by the Polish National Science Solving, vol 9. Kluwer Academic Publishers, Dordrecht Centre (NCN) Grants DEC-2011/01/D/ST6/06981, DEC-2012/05/B/ Pawlak Z, Skowron A (2007) Rudiments of rough sets. Inf Sci ST6/03215, DEC-2013/09/B/ST6/01568 as well as by the Polish 177(1):3–27 National Centre for Research and Development (NCBiR) under the Pearl J (2009) Causal inference in statistics: An overview. Stat Surv Grant O ROB/0010/03/001. Soma Dutta was supported by the 3:96–146 ERCIM postdoc fellowship. Pedrycz W (2013) Granular Computing Analysis and Design of Intelligent Systems. CRC Press/Taylor & Francis, Boca Raton Open Access This article is distributed under the terms of the Pedrycz W, Skowron A, Kreinovich V (eds) (2008) Handbook of Creative Commons Attribution 4.0 International License (http:// Granular Computing. Wiley, Hoboken

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Pfeifer R, Lungarella M, Iida F (2007) Self-organization, embodi- Stefanowski J (eds) Big Data Analysis. Studies in Big Data. ment, and biologically inspired robotic. Science 318:1088–1093 Springer, Heidelberg (in print) Polkowski L, Skowron A (2001) Rough mereological calculi of Slovik P, Courne`de (2011) Macroeconomic impact of Basel III. Working granules: A rough set approach to computation. Comput Intell Papers, vol 844. OECD Economics Publishing, OECD Economics Int J 17(3):472–492 Department. http://www.oecd.org/eco/Workingpapers Rahwan I, Simari GR (2009) Argumentation in Artificial Intelligence. Thiele LP (2010) The Heart of Judgment: Practical Wisdom, Springer, Berlin Neuroscience, and Narrative. Cambridge University Press, Rozenberg G, Ba¨ck T, Kok J (eds) (2012) Handbook of Natural Cambridge Computing. Springer, Berlin Ulam S, Bednarek A (1990) On the theory of relational structures and Skowron A, Jankowski A (2015) Interactive granular computing. In: schemata for parallel computation. In: Analogies between Ciucci D, Wang G, Mitra S, Wu W (eds) International Joint Analogies: the Mathematical Reports of S.M. Ulam and his Conference on Rough Sets, Tianjin, China, Korea, November Los Alamos Collaborators, pp 477–508 20–23, 2015, Proceedings of the RSKT 2015. Lecture Notes in Valiant L (2013) Probably Approximately Correct. Nature’s Algo- Artificial Intelligence, vol 9436. Springer, Heidelberg, pp 50–61 rithms for Learning and Prospering in a Complex World. Basic Skowron A, Stepaniuk J (2004) Information granules and rough- Books. A Member of the Perseus Books Group, New York neural computing. In: Pal SK, Polkowski L, Skowron A (eds) Yao YY (2008) A unified framework of granular computing. In: Rough-Neural Computing: Techniques for Computing with Pedrycz W, Skowron A, Kreinovich V (eds) Handbook of Words. Cognitive Technologies, Springer, Heidelberg, pp 43–84 granular computing. Wiley, Hoboken, pp 401–410 Skowron A, Stepaniuk J (2005) Hierarchical modelling in searching Zadeh LA (1979) Fuzzy sets and information granularity. In: for complex patterns: Constrained sums of information systems. Advances in Fuzzy Set Theory and Applications. North-Holland, J Exp Theor Artif Intell 17:83–102 Amsterdam, pp 3–18 Skowron A, Wasilewski P (2010) An introduction to perception based Zadeh LA (1996) Fuzzy logic = computing with words. IEEE Trans computing. In: Kim TH, Lee YH, Kang BH, S´le¸zak D (eds) Fuzzy Syst 4:103–111 Proceedings of FGIT 2010. Lectures Notes in Computer Science, Zadeh LA (1997) Toward a theory of fuzzy information granulation vol 6485. Springer, Heidelberg, pp 12–25 and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Skowron A, Wasilewski P (2011) Information systems in modeling Syst 90:111–127 interactive computations on granules. Theor Comput Sci Zadeh LA (2001) A new direction in AI: Toward a computational 412(42):5939–5959 theory of perceptions. AI Mag 22(1):73–84 Skowron A, Pal SK, Nguyen HS (eds) (2011) Special issue on rough Zadeh A (2012) Computing with Words: Principal Concepts and sets and fuzzy sets in natural computing. Theor Comput Sci Ideas. In: Studies in Fuzziness and Soft Computing, vol 277. 412(42):5815–5973 Springer, Heidelberg Skowron A, Jankowski A, Wasilewski P (2012) Risk management Zhong N, Ma JH, Huang R, Liu J, Yao Y, Zhang YX, Chen J (2013) and interactive computational systems. J Adv Math Appl Research challenges and perspectives on Wisdom Web of Things 1:61–73 (W2T). J Supercomput 64:862–882 Skowron A, Jankowski A, Dutta S (2015) Toward problem solving support based on big data and domain knowledge: Interactive granular computing and adaptive judgement. In: Japkowicz N,

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