Supporting Fuzzy Rough Sets in Fuzzy Description Logics

Classical Description Logics (DLs) are not suitable to represent vague pieces of information. The attempts to achieve a solution have lead to the birth of fuzzy DLs and rough DLs. In this work, we provide a simple solution to join these two formalisms and define a fuzzy rough DL. We also show how to extend two reasoning algorithms for fuzzy DLs, which are implemented in the fuzzy DL reasoners fuzzyDL and DeLorean .

[1]  Michel C. A. Klein,et al.  Rough Description Logics for Modeling Uncertainty in Instance Unification , 2007, URSW.

[2]  Fernando Bobillo,et al.  Optimizing the Crisp Representation of the Fuzzy Description Logic SROIQ , 2007, URSW.

[3]  Fernando Bobillo,et al.  A Crisp Representation for Fuzzy with Fuzzy Nominals and General Concept Inclusions. , 2008 .

[4]  Thomas R. Gruber,et al.  A Translation Approach to Portable Ontologies , 1993 .

[5]  Boris Motik,et al.  OWL 2: The next step for OWL , 2008, J. Web Semant..

[6]  Umberto Straccia,et al.  fuzzyDL: An expressive fuzzy description logic reasoner , 2008, 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence).

[7]  Umberto Straccia,et al.  Fuzzy description logics under Gödel semantics , 2009, Int. J. Approx. Reason..

[8]  Lipika Dey,et al.  A Rough-Fuzzy Ontology Generation Framework and Its Application to Bio-medical Text Processing , 2007, AWIC.

[9]  Fernando Bobillo,et al.  DeLorean: A Reasoner for Fuzzy OWL 1.1 , 2008, URSW.

[10]  Diego Calvanese,et al.  The Description Logic Handbook: Theory, Implementation, and Applications , 2003, Description Logic Handbook.

[11]  Umberto Straccia,et al.  Description Logics with Fuzzy Concrete Domains , 2005, UAI.

[12]  Thomas Lukasiewicz,et al.  Representing Uncertain Concepts in Rough Description Logics via Contextual Indiscernibility Relations , 2008, URSW.

[13]  Anna Maria Radzikowska,et al.  A comparative study of fuzzy rough sets , 2002, Fuzzy Sets Syst..

[14]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[15]  Dave Robertson,et al.  Probabilistic Dialogue Models for Dynamic Ontology Mapping , 2006, URSW.

[16]  Michel C. A. Klein,et al.  Description Logics with Approximate Definitions - Precise Modeling of Vague Concepts , 2007, IJCAI.

[17]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[18]  Elie Sanchez,et al.  Fuzzy Logic and the Semantic Web , 2005 .

[19]  Petr Hájek,et al.  Making fuzzy description logic more general , 2005, Fuzzy Sets Syst..

[20]  Umberto Straccia,et al.  Managing uncertainty and vagueness in description logics for the Semantic Web , 2008, J. Web Semant..

[21]  Fernando Bobillo,et al.  A Crisp Representation for Fuzzy SHOIN with Fuzzy Nominals and General Concept Inclusions , 2006, URSW.

[22]  Umberto Straccia,et al.  Reasoning within Fuzzy Description Logics , 2011, J. Artif. Intell. Res..

[23]  G. Stamou,et al.  Reasoning with Very Expressive Fuzzy Description Logics , 2007, J. Artif. Intell. Res..

[24]  Thomas R. Gruber,et al.  A translation approach to portable ontology specifications , 1993, Knowl. Acquis..

[25]  Ju Wang,et al.  Reasoning within expressive fuzzy rough description logics , 2009, Fuzzy Sets and Systems.

[26]  Fernando Ortega.  Managing vagueness in ontologies , 2011 .

[27]  Umberto Straccia,et al.  Managing Uncertainty and Vagueness in Description Logics, Logic Programs and Description Logic Programs , 2008, Reasoning Web.

[28]  Patrick Doherty,et al.  Towards a Framework for Approximate Ontologies , 2003, Fundam. Informaticae.

[29]  Peter F. Patel-Schneider,et al.  Reducing OWL entailment to description logic satisfiability , 2004, Journal of Web Semantics.

[30]  Suqin Tang,et al.  Reasoning with rough description logics: An approximate concepts approach , 2008, Information Sciences.

[31]  Lotfi A. Zadeh,et al.  Please Scroll down for Article International Journal of General Systems Fuzzy Sets and Systems* Fuzzy Sets and Systems* , 2022 .

[32]  Umberto Straccia,et al.  A fuzzy description logic for the semantic web , 2006, Fuzzy Logic and the Semantic Web.