An axiomatic approach of fuzzy rough sets based on residuated lattices

Abstract

Rough set theory was developed by Pawlak as a formal tool for approximate reasoning about data. Various fuzzy generalizations of rough approximations have been proposed in the literature. As a further generalization of the notion of rough sets, L -fuzzy rough sets were proposed by Radzikowska and Kerre. In this paper, we present an operator-oriented characterization of L -fuzzy rough sets, that is, L -fuzzy approximation operators are defined by axioms. The methods of axiomatization of L -fuzzy upper and L -fuzzy lower set-theoretic operators guarantee the existence of corresponding L -fuzzy relations which produce the operators. Moreover, the relationship between L -fuzzy rough sets and L -topological spaces is obtained. The sufficient and necessary condition for the conjecture that an L -fuzzy interior (closure) operator derived from an L -fuzzy topological space can associate with an L -fuzzy reflexive and transitive relation such that the corresponding L -fuzzy lower (upper) approximation operator is the L -fuzzy interior (closure) operator is examined.