Single axioms for (S, T)-fuzzy rough approximation operators with fuzzy product operations

Abstract

There are two different perspectives to study single axioms for (S, T)-fuzzy rough approximation operators, that is, ordinary fuzzy operations and fuzzy product operations. However, it is too complex and tedious to characterize (S, T)-fuzzy rough approximation operators with ordinary fuzzy operations, such as intersection, union and so on. To remedy these defects, this paper further investigates single axioms for (S, T)-fuzzy rough approximation operators with fuzzy product operations, where fuzzy relation is not limited into either a general fuzzy relation or a symmetric one. Considering a left-continuous t-norm T, we describe T-upper fuzzy rough approximation operators with fuzzy product operations by only one axiom. When t-conorm S is right-continuous and fuzzy negation N is strict, S-lower fuzzy rough approximation operators are characterized with fuzzy product operations by a single axiom.