Fuzzy Product Rough Sets as a Special Case of Fuzzy T-Rough Sets

Abstract

Fuzzy T-rough set consists of a set ???? and a T-similarity relation on ????, where T is a lower semicontinuous triangular norm. In this paper, axiomatic definition for fuzzy ????-rough sets and its upper approximation operator were proposed. The method employed was by relaxing the arbitrary T and adopting its special case ???????? (product triangular norm). The results obtained suggests an easier way of being specific  to the product case of fuzzy rough sets and computations regarding its upper approximation operators. Some important propositions and examples were also provided.