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 (υ σ)-fuzzy rough approximation operators are explored where υ is a residuated implicator and σis its dual implicator. Firstly, we review the existing independent axiomatic sets to characterize various types of υ-lower and σ-upper fuzzy rough approximation operators. Secondly, we present one-axiom characterizations of (υ σ)-fuzzy rough approximation operators constructed by a serial fuzzy relation on two universes. Furthermore, we show that (υ σ)-fuzzy rough approximation operators, corresponding to reexive, 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.
Axiomatic Characterizations of IVF Rough Approximation Operators
