L-fuzzifying approximation operators derived from general L-fuzzifying neighborhood systems

Abstract

For a completely distributive De Morgan algebra L, we develop a general framework of L-fuzzy rough sets. Said precisely, we introduce a pair of L-fuzzy approximation operators, called upper and lower L-fuzzifying approximation operators derived from general L-fuzzifying neighborhood systems. It is shown that the proposed approximation operators are a common extension of the L-fuzzifying approximation operators derived from L-fuzzy relations (INS 2019) and the approximation operators derived from general neighborhood systems (KBS 2014). Furthermore, we investigate the unary, serial, reflexive, transitive and symmetric conditions in general L-fuzzifying neighborhood systems, and then study the associated approximation operators from both a constructive method and an axiomatic method. Particularly, for transitivity (resp., symmetry), we give two interpretations, one is an appropriate generalization of transitivity (resp., symmetry) for L-fuzzy relations, and the other is a suitable extension of transitivity (resp., symmetry) for general neighborhood systems. In addition, for some special L-fuzzifying approximation operators, we use single axiom to characterize them, respectively. At last, the proposed approximation operators are applied in the research of incomplete information system, and a three-way decision model based on them is established. To exhibit the effectiveness of the model, a practical example is presented.