Extending fuzzy soft sets with fuzzy description logics

Abstract

Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. However, it has been pointed out that classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. In order to handle these types of problem parameters, some fuzzy extensions of soft set theory are presented, yielding fuzzy soft set theory. Fuzzy description logics (DLs) are a family of logics which allow the representation of and the reasoning within structured knowledge affected by vagueness. In this paper we extend fuzzy soft sets with fuzzy DLs, i.e., present an extended fuzzy soft set theory by using the concepts of fuzzy DLs to act as the parameters of fuzzy soft sets. We define some operations for the extended fuzzy soft sets. Moreover, we prove that certain De Morgan’s laws hold in the extended fuzzy soft set theory with respect to these operations. In fact, the extended fuzzy soft set theory based on fuzzy DLs presented in this paper is a fuzzy extension of the extended soft set theory based on DLs.