This paper introduces the relations between covering and dicovering in the framework of
rough sets. The natural counterpart of a covering in textures is given by a family of pairs of …

Departing from a suitable categorical description of closure operators, this paper dualizes
this notion and introduces some basic properties of dual closure operators. Usually these …

The notion of interior operator is intimately related to that of neighbourhood operator. This
relationship is presented here in the form of an adjunction or Galois connection, in the sense …

In this paper, we consider the Alexandroff topology for texture spaces. We prove that there
exists a one-to-one correspondence between the Alexandroff ditopologies, and the reflexive …

In this paper, the dependence spaces are discussed for textural formal concepts considering
the method given by Ma et al. A complete congruence on a complete lattice is an …

The idea of a texture is motivated from the unit interval [0, 1] with the ordinary ordering of real
numbers. This motivation can be extended to the family of fuzzy subsets, namely, to the …

We study cowellpoweredness in the category QUnif QUnif of quasi-uniform spaces and
uniformly continuous maps. A full subcategory AA of QUnif QUnif is cowellpowered when the …

In this work, we discuss interior and closure operators on textures in the sense of Dikranjan–
Giuli. First, we define the category dfICL of interior–closure spaces and bicontinuous …

The basic motivation of the theory of textures is to find a convenient point-set based setting
for fuzzy sets. Recent works on textures show that they also provide a useful model for rough …

It is known that approximation operator and definability are two main tools in rough set
theory. These tools are also key concepts for texture spaces. The aim of this chapter is to …