M-fuzzifying rough sets via M-fuzzifying algebraic relations

Abstract

The aim of this paper is to study M-fuzzifying algebraic rough sets in a constructive approach. For this purpose, the notion of M-fuzzifying algebraic relation is introduced and a pair of lower and upper
M-fuzzifying approximation operators are presented. Several conditions ofM-fuzzifying algebraic relations such as seriality, (resp., primitive, weak) symmetry, reflexivity and (resp., strong) transitivity are characterized by M-fuzzifying algebraic approximation operators. Then relationships amongM-fuzzifying algebraic rough sets, M-fuzzifying convex structures and M-fuzzifying rough sets are investigated. Specifically, the category of reflexive and transitiveM-fuzzifying algebraic rough spaces is isomorphic to the category of M-fuzzifying convex spaces. The category of reflexive, symmetric and transitiveM-fuzzifying algebraic rough spaces is isomorphic to the category of reflexive, symmetric and transitive M-fuzzifying rough spaces. In particular, the category of reflexive, weakly symmetric and transitive M-fuzzifying algebraic rough spaces is isomorphic to the category of M-fuzzifying convex matroids.