The role of topological De Morgan algebra in the theory of rough sets is investigated. The rough implication operator is introduced in strong topological rough algebra that is a generalization of classical rough algebra and a topological De Morgan algebra. Several related issues are discussed. First, the two application directions of topological De Morgan algebras in rough set theory are descri...

The concept of closure operator is key in several branches mathematics. In this paper, operators are extended to relational structures, more specifically fuzzy relations the framework complete lattices. core work search for a suitable definition (strong) relation, that is, relation whose with systems one-to-one. study properties and helps narrow down exploration until an appropriate settled.

in this paper, the concept of k-regular fuzzy matrix as a general- ization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. this leads to the characterization of a matrix for which the regularity index and the index are identical. further the relation between regular, k-regular and regularity of powers of fuzzy matrices are dis- cussed.

1. Introduction. In [4]2 the elements of a Banach algebra are separated into various classes: the regular elements, the singular elements , the null divisors, the generalized null divisors, and so forth. These classes and their interrelations are then studied in detail. In [5] transformations between Banach spaces are studied and the classes of [4], after suitable generalization, are characteri...

Wavelet analysis is a powerful tool withmodern applications as diverse as: image processing, signal processing, data compression, data mining, speech recognition, computer graphics, etc. The aim of this paper is to introduce the concept of atomic decomposition of fuzzy normed linear spaces, which play a key role in the development of fuzzy wavelet theory. Atomic decompositions appeared in appli...

In this paper, we consider quotient structure and quotient difunctions in the context of interior and closure operators on textures in the sense of Dikranjan-Giuli. The generalizations of several results concerning separation and quotient mapping are presented. It is shown that the category of interior-closure spaces and bicontinuous difunctions has a T0 reflection. Finally, we introduce some c...

The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to ...

This paper continues our investigation on hedge albebras [6]. We extend hedge algebras by two additional operations corresponding to infimum and supremum of the so-called concept category of an element x, i.e. the set which is generated from x by means of the hedge operations. It is shown that every extended hedge algebra with a lattice of the primary generators is a lattice. In the symmetrical...

Let £ be a partially ordered linear normed space over the field of real numbers whose positive cone K has nonempty interior K0.1 A functional / in E*, the conjugate space of E, is called positive if f(K)^0 and/5^0. A semi-group V of linear operators on E is called positive if r(A7) QK. It will be assumed that T contains the identity operator. This note is concerned with the properties of positi...

Closure operators (and closure systems) play a significant role in both pure and applied mathematics. In the framework of fuzzy set theory, several particular examples of closure operators and systems have been considered (e.g. so-called fuzzy subalgebras, fuzzy congruences, fuzzy topology etc.). Recently, fuzzy closure operators and fuzzy closure systems themselves (i.e. operators which map fu...