What is Fuzzy Logic and Fuzzy Ontology

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Robert Fullér

What is fuzzy logic and fuzzy ontology?

KnowMobile National Workshop, October 30, 2008, Helsinki.

Thursday, March 4, 2010



Web Ontology Language

•The Web Ontology Language (OWL) is a

family of knowledge representation

languages for authoring ontologies, and is

endorsed by the World Wide Web

Consortium. This family of languages isbased on two semantics: OWL DL and

OWL Lite semantics that are based on

Description Logics.




Description logic

• Description logics (DL) are a family of

knowledge representation languages whichcan be used to represent the terminological

knowledge of an application domain in a

structured and formally well-understood

way. Today description logic has become a

cornerstone of the Semantic Web for its

use in the design of ontologies.




Semantic Web

• The Semantic Web is an evolving extension

of the World Wide Web in which the

semantics of information and services on

the web is defined, making it possible for

the web to understand and satisfy the

requests of people and machines to use the

web content. The Web is considered as auniversal medium for data, information, and

knowledge exchange.




Ontology

• An ontology consists of a hierarchical description of important classes (or concepts) in a particular domain,along with the description of the properties (of the instances) of each concept.

•Web content is then annotated by relying on the concepts defined in a specific domain ontology.

• An ontology is a specification of conceptualization.

• A conceptualization is an abstract, simplified view of the world that we wish to represent for some purpose. Every knowledge base, knowledge-based system, or knowledge- level agent is committed to some conceptualization,explicitly or implicitly.






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Source: W.C. Cho and D. Richards, Ontology construction and concept reuse withformal concept analysis for improved web document retrieval, Web Intelligence andAgent Systems: An international journal 5 (2007) 109–126

Concept lattice for concepts of the formal context.





The general Recall and Precision are inversely relate.








Description Logics with fuzzy

Domain• Web Ontology Language Description Logics (OWL DL) becomes less

suitable in domains in which the concepts to be represented have not a precise definition. As we have to deal with Web content, it is easily verifiedthat this scenario is, unfortunately, likely the rule rather than an exception.

• For instance, just consider the case we would like to build an ontology aboutflowers. Then we may encounter the problem of representing concepts like“Candia is a creamy white rose with dark pink edges to the petals”,“Jacaranda is a hot pink rose”, “Calla is a very large, long white flower onthick stalks”. As it becomes apparent such concepts hardly can be encodedinto OWL.

• As it becomes apparent such concepts hardly can be encoded into OWL DL,as they involve fuzzy or vague concepts, like “creamy”, “dark”, “hot”,“large” and “thick”, for which a clear and precise definition is impossible.




Fuzzy Ontology

• A fuzzy ontology is a quintuple F =< I, C,T,N,X > where

• I is the set of individuals (objects), also called instances of the concepts.

• C is a set of fuzzy concepts (or classes - cf. in OWL - of individuals, or categories, or types). Each concept is a fuzzy set on the domain of instances.

• The set of entities of the fuzzy ontology is defined by E = C ∪ I.

• T denotes the fuzzy taxonomy relations among the set of concepts C. It organizesconcepts into sub-(super-)concept tree structures. The taxonomic relationship T (i, j )indicates that the child j is a conceptual specification of the parent i with a certaindegree.

• N denotes the set of non-taxonomy fuzzy associative relationships that relate entitiesacross tree structures, for example:

- Naming relationships, describing the names of concepts- Locating relationships, describing the relative location of concepts- Functional relationships, describing the functions (or properties) of concepts

• X is the set of axioms expressed in a proper logical language, i.e., predicates thatconstrain the meaning of concepts, individuals, relationships and functions.




A fuzzy ontology scheme.

Source: David Tudor Parry: Fuzzy Ontology and Intelligent Systems for Discovery of Useful Medical

Information, Ph.D. Thesis, Auckland University of Technology, 2005.




Fuzzy Ontology Generation for Semantic Web.

Source: Quan Thanh Tho, Siu Cheung Hui, Automatic Fuzzy Ontology Generation for Semantic Web, IEEE TRANSACTIONS ON

KNOWLEDGE AND DATA ENGINEERING, VOL. 18, NO. 6, JUNE 2006

C = {”Document,” ”Research Area”}

Fuzzy formal context can also be

represented as a cross-table as shown in

Table 1.

The context has three objects representing

three documents, D1,D2,D3.

It also has three attributes Data Mining,

Clustering and Fuzzy Logic representing

three research topics.

The relationship between an object and anattribute is represented by a membership

value in [0,1].

An α-cut can be set to eliminate relations

that have low membership values.




A fuzzy ontology for wine

Taste(cabernet, very_dry)=0.7×0.7⇔ Cabernet has a very dry taste with value 0.49

Taste(cabernet, dry)=0.7⇔ Cabernet has a dry taste with value 0.7

Source: Silvia Calegari and Davide Ciucci,

INTEGRATING FUZZY LOGIC IN ONTOLOGIES, 8th

International Conference on Enterprise Information

Systems, 2006.

Taste(cabernet, not_dry)=1-0.7⇔ Cabernet has not a dry taste with value 0.3

Name of fuzzy relation: Taste

Name of instance: cabernet

Name of property: dry

Illustration of a non-taxonomic relation.

Some possible values:

Documents

What is Fuzzy Logic and Fuzzy Ontology