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A Model for Representing Vague Linguistic Terms and Fuzzy Rules for Classification in Ontologies

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A Model for Representing Vague Linguistic Terms and Fuzzy Rules for Classification in Ontologies A MODEL FOR REPRESENTING VAGUE LINGUISTIC TERMS AND FUZZY RULES FOR CLASSIFICATION IN ONTOLOGIES Cristiane A. Yaguinuma, Vinícius R. T. Ferraz, Marilde T. P. Santos, Heloisa A. Camargo Department of Computer Science, Federal University of São Carlos, Rod. Washington Luis Km 235, São Carlos, SP, Brazil {cristiane_yaguinuma, vinicius_ferraz, marilde, heloisa}@dc.ufscar.br Tatiane M. Nogueira Institute of Mathematics and Computer Sciences, University of São Paulo, Av. Trabalhador São-carlense, 400, São Carlos, SP, Brazil [email protected] Keywords: Knowledge Representation, Fuzzy Set Theory, Fuzzy Ontology, Fuzzy Reasoning, Classification Abstract: Ontologies have been successfully employed in applications that require semantic information processing. However, traditional ontologies are not able to express fuzzy or vague information, which often occurs in human vocabulary as well as in several application domains. In order to deal with such restriction, concepts of fuzzy set theory should be incorporated into ontologies so that it is possible to represent and reason over fuzzy or vague knowledge. In this context, this paper proposes a model for representing fuzzy ontologies covering fuzzy properties and fuzzy rules, and we also implement fuzzy reasoning methods such as classical and general fuzzy reasoning, aiming to support classification of new instances based on fuzzy rules. 1 INTRODUCTION ence based on fuzzy reasoning methods, e.g. classical and general methods (Cordón et al., 1999). There- Ontologies have been widely used in applications re- fore, such rules can be used to infer the classification garding knowledge representation, such as the Se- of elements into specific categories according to the mantic Web, which investigates the semantics of con- values of fuzzy variables. tent and services over the Web. In the context of com- In this sense, it is important that ontologies repre- puter and information sciences, an ontology defines a sent vague or fuzzy information and support approxi- set of representational primitives with which to model mate reasoning mechanisms. Hence, fuzzy reasoning a domain of knowledge or discourse (Gruber, 2009). methods should be associated to fuzzy ontologies, im- As ontologies model semantic elements and support proving the expressiveness of concepts and relation- reasoning, they have been applied to improve seman- ships modelled. Specifically, classification methods tic information processing among humans and com- based on fuzzy rules are useful to several applica- putational systems. tions, including Semantic Web and Text Mining, by Although expressive, the background formalism classifying contents (Web pages and documents) into of traditional ontologies is not able to represent im- concepts of a domain depending on fuzzy properties precise or vague information, which often occurs in associated to linguistic terms. human language and in several application domains. For example, it is difficult to model concepts like In order to face these issues, we propose a model young, dark, hot and large, for which a clear and pre- for representing fuzzy ontologies that considers the cise definition is not possible (Straccia, 2006). Fuzzy classic and general fuzzy reasoning methods for clas- sets (Zadeh, 1965) provide a meaningful and powerful sification based on rules containing fuzzy properties. representation of vague concepts expressed in natural This paper is organized as follows. Section 2 dis- language. Several fuzzy sets representing linguistic cusses related work on fuzzy ontology representa- concepts, such as low, medium and high, are often em- tion. Next, Section 3 describes the proposed model ployed to define states of a variable (fuzzy variable) for fuzzy ontology representation, followed by a case (Klir and Yuan, 1995). Such variables are often used study presented on Section 4. Finally, Section 5 con- in production rules, which support knowledge infer- cludes this paper and points future works. 2 RELATED WORK ON FUZZY 3 MODEL FOR FUZZY ONTOLOGY PROPERTIES AND RULES IN ONTOLOGIES In order to represent fuzzy class, fuzzy property and Among the approaches for fuzzy ontology repre- fuzzy rule, we present some definitions to compre- sentation, some researches consider ontologies com- hend how we have incorporated them in ontologies: posed of fuzzy classes and fuzzy relationships to rep- Definition 1. Fuzzy class, which corresponds to a resent the semantics of domains. In this case, fuzzy fuzzy set, is a class whose individuals can belong to it class and fuzzy relationship respectively correspond with a membership degree between the interval [0;1]. to fuzzy set and fuzzy relation of the fuzzy set theory When a fuzzy class corresponds to a fuzzy linguis- (Zadeh, 1965). Fuzzy OWL (Stoilos et al., 2006) and tic term associated to a continuous attribute, it can f-OWL DL (Pan et al., 2008) extend OWL language be defined by a parameterized membership function, elements in order to represent such features in ontolo- such as triangular and trapezoidal functions (Klir and gies. Yuan, 1995). Recently, fuzzy ontology approaches are mov- Definition 2. Fuzzy property is defined as a property ing forward to express fuzzy properties, membership or attribute that can assume vague linguistic values functions and linguistic hedges (Straccia, 2006; Cale- represented by fuzzy classes. This definition is based gari and Ciucci, 2007). Fuzzy properties or fuzzy on the fuzzy variable definition, which corresponds to datatypes extend attributes of traditional ontologies, a variable whose values are fuzzy linguistic terms. corresponding to fuzzy variables whose values can be Definition 3. Fuzzy rule is defined as an if-then rule vague linguistic terms defined as fuzzy sets. For ex- whose antecedent contains fuzzy properties and the ample, the age attribute can assume fuzzy linguistic consequent has a class defined in the ontology (clas- values such as young, adult or old that correspond sification rule). Fuzzy reasoning methods can be ap- to fuzzy sets. Linguistic hedges are special linguis- plied over these rules to derive the class of an individ- tic terms by which other terms are modified (Klir and ual based on the values of its fuzzy properties. Yuan, 1995). Terms like very, more or less, fairly are From these definitions, we propose the model il- classic examples of hedges. Any linguistic hedge may lustrated as a graph in Figure 1. In this model, the be interpreted as a unary operation on the unit interval Fuzzy Variable element is responsible for connecting [0;1]. By representing these fuzzy semantic elements, a Fuzzy Property to its linguistic terms represented as ontologies can model a semantics closely related to Membership Function Fuzzy Class. Such connection the vagueness of human vocabulary. is respectively made by hasFuzzyProperty and has- FuzzyValue relationships. The Membership Function Some researches have also pointed to fuzzy rule Fuzzy Class is a fuzzy class that is defined by a pa- representation. For example, Damásio et al. (Damá- rameterized membership function. This class can rep- sio et al., 2008) extend the RuleML language to ex- resent a linguistic term, whose label is described by press degrees of truth assigned to propositons and linguisticLabel property of type String. The Trape- rules, however their approach do not support fuzzy zoidal and Triangular subclasses represent two possi- properties and membership functions. Fuzzy DL sys- ble parameterized membership functions that can be tem (Bobillo and Straccia, 2008) has achieved better used to model a fuzzy class. To define more param- expressiveness, as it represents fuzzy rules contain- eterized functions, subclasses can be added as well. ing linguistic terms and implements reasoning mech- Finally, the parameters of membership functions are anisms based on Mamdani method. represented by leftZeroParameter, leftOneParameter, As the review of the literature shows, there is a rightZeroParameter, rightOneParameter properties of growing trend to increase expressiveness in fuzzy on- type float. These parameters determine which values tologies. Following this direction, it is interesting that of the fuzzy property that the membership function fuzzy ontologies support reasoning mechanisms to- assumes minumum (zero) and maximum (one) val- wards classification based on rules containing fuzzy ues, both considering left and right sides of the trapez- properties. Aiming to support these features, it is fun- ium. In case of triangular functions, only three pa- damental to represent fuzzy properties, membership rameters are required, with leftOneParameter corre- functions and rules in a suitable way. In this sense, sponding to the center of the triangle. Section 3 describes the proposed model for represent- An important feature of the proposed model is that ing fuzzy properties and classification rules for further it is an abstract representation, thus independent of fuzzy reasoning in ontologies. ontology language syntax. So, it can be instantiated Figure 1: Model for representing fuzzy properties and their linguistic terms as parameterized fuzzy classes. using any traditional ontology language that models properties of documents. Last column contains the representational primitives such as classes, instances, document class assigned by domain experts, where attributes and relationships. This is a relevant contri- FL stands for Fuzzy Logics, M for Mining and ML for bution in comparison to related work, since existing Machine Learning. All these categories correspond to approaches
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