Generalized closed sets in ditopological texture spaces with application in rough set theory

Abstract

In this paper, the counterparts of generalized open (g-open) and generalized closed (g-closed) sets for ditopological texture spaces are introduced and some of their characterizations are obtained. Some characterizations are presented for generalized bicontinuous difunctions. Also, we introduce new notions of compactness and stability in ditopological texture spaces based on the notion of g-open and g-closed sets. Finally, as an application of g-open and g-closed sets, we generalize the subsystem based denition of rough set theory by using new subsystem, called generalized open sets to dene new types of lower and upper approximation operators, called g-lower and g-upper approximations. These decrease the upper approximation and increase the lower approximation and hence increase the accuracy. Properties of these approximations are studied. An example of multi-valued information systems are given.