On Simplified Axiomatic Characterizations of (θ, σ)-Fuzzy Rough Approximation Operators

The axiomatic approach is more appropriate than constructive approach for studying the algebraic structure of rough sets. In this paper, the more simple axiomatic characterizations of (theta, sigma)-fuzzy rough approximation operators are explored where u is a residuated implicator and sigma is its dual implicator. Firstly, we review the existing independent axiomatic sets to characterize various types of 19-lower and a-upper fuzzy rough approximation operators. Secondly, we present one-axiom characterizations of (theta, sigma)-fuzzy rough approximation operators constructed by a serial fuzzy relation on two universes. Furthermore, we show that (theta, sigma)-fuzzy rough approximation operators, corresponding to reflexive, symmetric and T-transitive fuzzy relations, can be presented by only two axioms respectively. We conclude the paper by introducing some potential applications and future works.