Fuzzy rough set models over two universes using textures

Abstract

The purpose of this paper is twofold: firstly, to exhibit the existence of a reasonable connection between fuzzy relations and (textural) fuzzy direlations in terms of fuzzy logical connectives; and secondly, to give a new perspective with respect to approximation operators due to fuzzy rough set models over two universes using textures. To this end, we investigate the serialities of fuzzy relations in terms of fuzzy logic connectives using fuzzy direlations. For different fuzzy logic systems, we show that the textural serialities provide alternative descriptions of the serialities of a fuzzy relation in terms of parameters. Without considering the motivation of the semantic link with the classical Pawlak rough sets, we obtain and discuss the natural fuzzifications of rough set models over two universes. Further, we execute that a textural fuzzy rough set model is an efficient template for the basic properties of the various fuzzy rough set models over two universes. For instance, we prove that the revised fuzzy rough set approximations with two universes are the natural extensions of the loose and tight approximations of De Cock et al.