A fuzzy extension of description logic script A sign ℒ script C sign script H sign

Abstract

Based on the idea that the cut sets of fuzzy sets are indeed crisp, but facilitate a normative theory for formalizing fuzzy set theory, this paper introduces cut sets of the fuzzy concepts and fuzzy roles as atomic concepts and atomic roles to build script E sign script F sign script A sign ℒ script C sign script H sign, a new fuzzy extension of script A sign ℒ script C sign script H sign. This paper gives the definition of syntax, semantics and knowledge base of script E sign script F sign script A sign ℒ script C sign script H sign and discusses the comparison among script E sign script F sign script A sign ℒ script C sign script H sign and other fuzzy extensions of script A sign ℒ script C sign script H sign. In addition, this paper defines the acyclic TBox form of script E sign script F sign script A sign ℒ script C sign script H sign, presents sound and complete algorithms for reasoning tasks w.r.t acyclic TBox, and proves the complexity of them is PSPACE-complete. © Springer-Verlag Berlin Heidelberg 2005.