Extended Fuzzy Description Logics with Comparisons Between Fuzzy Membership Degrees

Abstract

语义Web模糊知识的表示和应用常常涉及模糊隶属度比较,但现有描述逻辑的模糊扩展缺乏描述模糊隶属度比较的能力.提出支持模糊隶属度比较和描述逻辑ALCN(attributive concept description language with complements and number restriction)概念构造子的扩展模糊描述逻辑FCALCN(fuzzy comparable ALCN).FCALCN引入新的原子概念形式以支持模糊隶属度比较.给出FCALCN的推理算法,证明了在空TBox约束下FCALCN的推理问题复杂性是多项式空间完全的.FCALCN能够表达语义Web上涉及模糊隶属度比较的复杂模糊知识并实现对它们的推理.;The representation and application of fuzzy knowledge on the semantic Web often relate to the comparisons between fuzzy membership degrees. However, the current fuzzy extensions of description logics do not support the expression of such comparisons. This paper proposes an extended fuzzy description logic that supports the comparisons of fuzzy membership degrees and the concept constructors from description logic ALCN (attributive concept description language with complements and number restriction), written FCALCN (fuzzy comparable ALCN). FCALCN introduces new forms of atom concepts in order to support the comparisons between fuzzy membership degrees. A reasoning algorithm for FCALCN is proposed, and the complexity of the reasoning problems of FCALCN with empty TBox is proved to be PSpace-complete. FCALCN can represent expressive fuzzy knowledge involving the comparisons of fuzzy membership degrees on the semantic Web and enable reasoning of them.