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Integrating Fuzzy Logic in Ontologies INTEGRATING FUZZY LOGIC IN ONTOLOGIES Silvia Calegari and Davide Ciucci Dipartimento di Informatica, Sistemistica e Comunicazione, Universita` degli Studi di Milano Bicocca, via Bicocca degli Arcimboldi 8, 20126 Milano, Italy Keywords: Concept modifiers, fuzzy logics, fuzzy ontologies, membership modifiers, KAON, ontology editor. Abstract: Ontologies have proved to be very useful in sharing concepts across applications in an unambiguous way. Nowadays, in ontology-based applications information is often vague and imprecise. This is a well-known problem especially for semantics-based applications, such as e-commerce, knowledge management, web por- tals, etc. In computer-aided reasoning, the predominant paradigm to manage vague knowledge is fuzzy set theory. This paper presents an enrichment of classical computational ontologies with fuzzy logic to create fuzzy ontologies. So, it is a step towards facing the nuances of natural languages with ontologies. Our pro- posal is developed in the KAON ontology editor, that allows to handle ontology concepts in an high-level environment. 1 INTRODUCTION A possible solution to handle uncertain data and, hence, to tackle these problems, is to incorporate fuzzy logic into ontologies. The aim of fuzzy set An ontology is a formal conceptualization of a partic- theory (Klir and Yuan, 1995) introduced by L. A. ular domain of interest shared among heterogeneous Zadeh (Zadeh, 1965) is to describe vague concepts applications. It consists of entities, attributes, rela- through a generalized notion of set, according to tionships and axioms to provide a common under- which an object may belong to a certain degree (typ- standing of the real world (Lammari and Mtais, 2004; ically a real number from the interval [0,1]) to a set. Gruber, 1993; Guarino and Giaretta, 1995). With the For instance, the semantic content of a statement like support of ontologies, users and systems can commu- “Cabernet is a deep red acidic wine” might have de- nicate with each other through an easier information gree, or truth-value, of 0.6. Up to now, fuzzy sets and exchange and integration (Soo and Lin, 2001). On- ontologies are jointly used to resolve uncertain infor- tologies help people and machines to communicate mation problems in various areas, for example, in text concisely by supporting information exchange based retrieval (Bouquet et al., 2004; Singh et al., 2004; Ab- on semantics rather than just syntax. ulaish and Dey, 2003) or to generate a scholarly on- There are ontological applications where informa- tology from a database in ESKIMO (Matheus, 2005) tion is often vague and imprecise. For instance, and FOGA (Quan et al., 2004) frameworks. However, the semantic-based applications of the Semantic Web in none of these examples there is a fusion of fuzzy set (Berners-Lee et al., 2001), such as e-commerce, theory with ontologies. knowledge management, web portals, etc. Indeed, the conceptual formalism supported by a typical ontol- The aim of this paper is to present a proposal to di- ogy may not be sufficient to represent uncertain infor- rectly integrate fuzzy logic in ontology in order to ob- mation that is commonly found in many application tain an extension of the ontology that is more suitable domains. For example, keywords extracted by many for solving uncertainty reasoning problems. It is a queries in the same domain may not be considered first step towards the realization of a theoretical model with the same relevance, as some keywords may be and of a complete framework based on ontologies that more significant than others. Therefore, the need of are able to consider the nuances of natural languages. giving a different interpretation according to the con- In literature, a first tentative has been made in the text emerges. context of medical document retrieval (Parry, 2004) 66 Calegari S. and Ciucci D. (2006). INTEGRATING FUZZY LOGIC IN ONTOLOGIES. In Proceedings of the Eighth International Conference on Enterprise Information Systems - AIDSS, pages 66-73 DOI: 10.5220/0002496100660073 Copyright c SciTePress INTEGRATING FUZZY LOGIC IN ONTOLOGIES by adding a degree of membership to all terms in the 2.1 Defining a Fuzzy Value ontology to overcome the overloading problem. An- other proposal is an extension of the domain ontology The first problem to tackle is how to assign a fuzzy with fuzzy concept (Chang-Shing et al., 2005), how- value to an entity of the ontology. The trade off is be- ever only for Chinese news summarization. tween understandability and precision, since (Casillas This paper shows how to insert fuzzy logic during et al., 2003) ontology creation with KAON (KAON, 2005). This to obtain high degree of interpretability and ac- software consists in a number of different modules curacy is a contradictory purpose and, in prac- providing a broad range of functionalities centered tice, one of the two properties prevails over the around creation, storage, retrieval, maintenance and other one. Depending on what requirement is application of ontologies. KAON allows the use of mainly pursued, the Fuzzy Modelling field may an ontology at high-level, and the relative conceptual be divided into two different areas: models are defined in a natural and easily understand- able way. 1. Linguistic fuzzy modelling – The main objec- The rest of the paper is organized as follows: Sec- tive is to obtain fuzzy models with a good in- tion 2 defines a fuzzy ontology and explains how to terpretability define and use fuzzy values in it. Section 3 presents 2. Precise fuzzy modelling – The main objective the ontology editor used and it is shown how to in- is to obtain fuzzy models with a good accu- tegrate it with our framework. In Section 4, we give racy. an overview on related works and on the next steps of Since our goal is to be as general as possible, both our approach. the possibilities are given to the expert: define a precise value or a linguistic one. In the former case the expert, while creating the ontology, de- 2 FUZZY LOGIC fines a function f :(Concepts ∪ Instance) × P roperties → Property Value× [0, 1] with the ( ) In this section, we present a logical framework to sup- meaning that f o, p is the value that a concept or port and to reason with uncertainty. This is a focus an instance o assumes for property p with associated aspect for all ontology-based applications where the degree. For example, in an hypothetical ontology of user is interested in information that often contains cats, f(Garfield,color) = (orange,0.8) means that for imprecise and vague description of concepts. For ex- the property color, the instance Garfield, has value or- ample, one may be interested in finding “a very strong ange with degree 0.8. Or, in a wine ontology, f(wine, flavored red wine” or in reasoning with concepts such taste)= (full-bodied,0.4) means that the concept wine as “a cold place”, “an expensive item”, “a fast motor- has a full-bodied (the value) taste (the property) with cycle”, etc. degree 0.4. In order to face these problems the proposed ap- Clearly, there may exist situations in which no proach is based on fuzzy sets theory. It has not been property value is necessary for a given property. For example, “Garfield has sense of humour with chosen a particular ontology domain to explain our 0 9 theory because our goal is to fulfil all nuances of nat- value . ” cannot be correctly expressed with the ural languages and to take into account all the differ- just exposed formalism. In this situation, it is neces- sary to map a pair (concept/instance, property) sim- ent aspects that an ontology have to consider. Our [0 1] :( ∪ ) × aim is to extend an ontology editor to directly handle ply to , , i.e., f Concept Instance P roperties → [0, 1] and the above example becomes uncertainty during the ontology definition, so that to enrich the knowledge domain. f (Garfield,sense of humour) = 0.9. At first, let us remind the definition of a fuzzy set. In order to simplify the nota- tion, we can define a unique function Let us consider a nonempty set of objects U, called :( ∪ ) × ( ∪ the universe.Afuzzy set or generalized characteris- g Concepts Instances P roperties [0 1] Prop val) → [0, 1]. Thus, “Garfield has color tic functional is defined as a , –valued function on 0 8 U, f : U → [0, 1]. Given an object x ∈ U, f(x) orange with value . ” becomes g(Garfield,orange) = represents the membership value of x to the set f.In 0.8. Using these function g, the expert has the chance the following of this section we explain how to intro- to choose a membership value with infinite accuracy, duce fuzzy values on different objects of an ontology that is precision is preferred to interpretability. and how to automatically correct them. Finally, we On the other hand, the second possibility is to choose as membership value, a label in a given set. give some hint on the possible applications of a fuzzy ={ ontology. We have chosen the set L little, enough, moder- ately, quite, very, totally} which is clearly not exhaus- tive of all the possible labels, but it can intuitively be modified as desidered. 67 ICEIS 2006 - ARTIFICIAL INTELLIGENCE AND DECISION SUPPORT SYSTEMS In this case the value g(o, p) is automatically as- 2.2 Updating a Fuzzy Value signed according to Table 1. Once an expert has created a fuzzy ontology, it is not realistic to assume that it is perfect and that any fuzzy Table 1: assignement of fuzzy value to labels. value is well-defined and suited to any environment. Thus, a mechanism to change fuzzy values in order to Label Value fit them in the best way to a specific environment or, in little 0.2 general, to make them more correct is needed.
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