Granul. Comput. (2016) 1:95–113 DOI 10.1007/s41066-015-0002-1 ORIGINAL PAPER Interactive granular computing 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 rough set-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