Fuzzy Ontology Model for Knowledge Management Jun Zhai Lixin Shen Zhou Zhou Yan Liang School of Economics and Management, Dalian Maritime University, Dalian 116026, P. R. China Abstract Lee et al. [6] proposed an algorithm to create fuzzy ontology and applied it to news summarization. Ontology is the basis of sharing and reusing This work is based on their previous work on knowledge on the semantic web. The fuzzy ontology ontology-based fuzzy event extraction agents for is an extension of the domain ontology for solving the Chinese news summarization [7]. Tho et al. proposed uncertainty problems. Current fuzzy ontology models a Fuzzy Ontology Generation Framework (FOGA) for do not focus on essential semantic relationships fuzzy ontology generation on uncertainty information between fuzzy concepts, which lead difficulty in [8]. This framework is based on the idea of fuzzy ontology integrating. To represent formally the fuzzy theory and Formal Concept Analysis (FCA). knowledge, this paper proposes a series of fuzzy Abulaishet et al. [9] proposed a fuzzy ontology ontology models that consist of fuzzy domain framework in which a concept descriptor is ontology and fuzzy linguistic variable ontologies, represented as a fuzzy relation which encodes the considering semantic relationships of concepts, degree of a property value using a fuzzy membership including set relation, order relation and equivalence function. To enable representation and reasoning for relation. Application of the fuzzy ontology to fuzzy ontologies, Kang et al. [10] proposed a new transportation knowledge modeling shows that this fuzzy extension of description logics called the fuzzy research facilitates the knowledge share and reuse for description logics with comparison expressions fuzzy systems on the semantic web. (FCDLs). But, current fuzzy ontology models do not focus Keywords: Ontology, Fuzzy ontology, Fuzzy system, on essential semantic relationships between fuzzy Knowledge management concepts, which lead difficulty in ontology mapping and integrating. To represent formally the fuzzy knowledge, this paper proposes a new kind of fuzzy 1. Introduction ontology models. The rest of this paper is organized as Ontology is a conceptualization of a domain into a follows: Section 2 introduces fuzzy domain ontology human understandable, machine-readable format model. Section 3 proposes fuzzy linguistic variable consisting of entities, attributes, relationships, and ontology model, extended fuzzy ontology model and axioms [1]. It is used as a standard knowledge basic fuzzy ontology model. Section 4 applies the representation for the Semantic Web [2]. However, the fuzzy ontology to transportation knowledge modeling. conceptual formalism supported by typical ontology Finally, section 5 concludes the paper. may not be sufficient to represent uncertainty information commonly found in many application 2. Fuzzy domain ontology model domains due to the lack of clear-cut boundaries between concepts of the domains. Moreover, fuzzy An ontology ( O ) organizes domain knowledge in knowledge plays an important role in many domains terms of concepts ( C ), properties ( P ), relations ( R ) that face a huge amount of imprecise and vague and axioms ( A ), and can be formally defined as knowledge and information, such as text mining, follows. multimedia information system, medical informatics, Definition 1 (Ontology) – An ontology is a 4- machine learning, and human natural language tuple O = (C, P, R, A) , where: processing [3]. To handle uncertainty of information and 1. C is a set of concepts defined for the domain. A knowledge, one possible solution is to incorporate concept is often considered as a class in an ontology. fuzzy theory into ontology. Then we can generate 2. P is a set of concept properties. A property p ∈ P fuzzy ontologies, which contain fuzzy concepts and is defined as an instance of a ternary relation of the fuzzy memberships. The fuzzy ontologies are capable form p(c,v, f ) , where c ∈ C is an ontology of dealing with fuzzy knowledge [4], and are efficient in text and multimedia object representation and concept, v is a property value associated with c and retrieval [5]. f defines restriction facets on v . Some of the restriction facets are – type ( ft ), cardinality ( f c ), and where c ∈ C is an ontology concept, vF represents range ( f r ). The type facet f t may be any one from property values , qF models linguistic qualifiers, the standard data types supported by ontology editors, which can control or alter the strength of a property value v , f is the restriction facets on v , and i.e. f t ∈ {boolean, integer, float, string, symbol, F F U is the universe of discourse. Both v and q are instance, class, …}. The cardinality facet f c defines F F the upper and lower limits on the number of values for the fuzzy concepts at U , but qF changes the fuzzy the property. The range facet f specifies a range of r degree of vF . For example, “price” is a property of values that can be assigned to the property. concept “fruit”. The value of “price” may be either fuzzy concept “cheap” or fuzzy number “around 50”, 3. R = {r | r ⊆ C × C × Rt } is a set of binary and the linguistic qualifiers may be “very”, “little”, semantic relations defined between concepts in C . “close to” etc. Therefore, the final value of “price” Rt = {one-to-one, one-to-many, many-to-many} is may be “very cheap” or “little expensive”. the set of relation type. 3. RF is a set of inter-concept relations between A set of basic relations is defined as {synonym concepts. Like fuzzy concept properties, rF ∈ RF is of, kind of, part of, instance of, property of} ⊂ R defined as a 5-tuple of the form , which have the following interpretations: rF (c1 ,c2 ,t, sF ,U ) where c ,c ∈ C are ontology concepts, t (1) ci synonym of c j : ci is equivalent to c j . The 1 2 synonym relation of natural language is modeled in an represents relation type, U is the universe of ontology using the equivalence relation. If two discourse , and sF models relation strengths and is concepts ci and c j are declared equivalent in an fuzzy concept at U , which can represent the strength of association between concept-pairs < c ,c > . ontology then instances of concept ci can also be 1 2 4. A is a set of fuzzy rules. In a fuzzy system the set inferred as instances of c j and vice-versa. F of fuzzy rules is used as knowledge base. (2) c j kind of ci : ci is a generalization of c j . When The fuzzy domain ontology is used to model an ontology specifies that c is a generalization of domain expert knowledge. But, due to the lack of i relationships between fuzzy concepts that can be the c j , then c j inherits all property descriptors value of properties, it is difficult to integrate diverse ontology systems. For example, in an ontology the set associated with , and these need not be repeated for ci of property “price” value is {cheap, appropriate, c j while specifying the ontology. expensive, …}, and in other ontology the same set is {high, low, middle, …}. To map these ontologies, it is (3) c j part of ci : ci has part c j . In an ontology, a necessary to define the semantic relationship between concept which is defined as aggregation of other fuzzy concepts, e.g. “cheap” and “expensive” have the concepts is expressed using this relation. relation of disjointness, and “low” and “high” have the (4) c instance of c : c is an instance of c . same relation of disjointness etc. j i j i Consequently, we propose the fuzzy linguistic (5) c j property of ci : c j is a property of ci . variables ontology models. 4. A is a set of axioms. An axiom is a real fact or reasoning rule. 3. Fuzzy linguistic variable ontology The fuzzy ontology is created as an extension to The fuzzy linguistic variables proposed by Zadeh are the standard ontology. the basic of fuzzy knowledge and fuzzy system [3]. To Definition 2 (Fuzzy domain ontology) – A fuzzy achieve the knowledge share and reuse for fuzzy domain ontology is a 4-tuple OF = (C, PF , RF , AF ) , systems on the semantic web, it is necessary to where: represent the fuzzy linguistic variables with ontology. 1. C is a set of concepts. Differing from definition 1, Definition 3 (Fuzzy linguistic variable) – Fuzzy every concept here has some properties whose value is linguistic variable is the variable whose value is term fuzzy concept or fuzzy set. or concept in natural language. A fuzzy linguistic variable is a 4-tuple (X ,T, M ,U ) , where: 2. PF is a set of properties. A property pF ∈ PF is defined as a 5-tuple of the form p (c,v ,q , f ,U ) , 1. X is the name of fuzzy linguistic variable, e.g. F F F “price” or “speed” etc. 2. T is the set of terms which is the value of fuzzy To simplify the transform from fuzzy linguistic linguistic variable, e.g. T ={ cheap, appropriate, variables to fuzzy ontology, we introduce the basic expensive, …} or T ={fast, middle, slow,…}. fuzzy ontology model as follows. Definition 6 (Basic fuzzy ontology) –A basic 3. M is the mapping rules which map every term of fuzzy ontology is a 4-tuple O = (c ,C , F,U ) , T to fuzzy set at U . F a F 4. U is the universe of discourse. where ca ,CF , F,U have same interpretations as Introducing semantic relationships between defined in definition 4, which satisfy the following concepts, we obtain the ontology model. conditions: Definition 4 (Fuzzy linguistic variable ontology) 1. C = {c ,c , ,c } is a limited set. – A fuzzy linguistic variable ontology is a 5-tuple F 1 2 L n 2.