in this paper, the notion of fuzzy semicompactness degrees isintroduced in $l$-fuzzy topological spaces by means of theimplication operation of $l$. characterizations of fuzzysemicompactness degrees in $l$-fuzzy topological spaces  areobtained, and some properties of fuzzy semicompactness degrees areresearched.

The purpose of this paper is to introduce and study the concepts of fuzzy $e$-open set, fuzzy $e$-continuity and fuzzy $e$-compactness in intuitionistic fuzzy topological spaces. After giving the fundamental concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy $e$-open sets and intuitionistic fuzzy $e$-continuity and other results re...

This paper is devoted to the study of intuitionistic fuzzy topological spaces. In this paper an intuitionistic fuzzy regular weakly generalized closed set and intuitionistic fuzzy regular weakly generalized open set are introduced. Some of its properties are studied. Also we have provided some applications of intuitionistic fuzzy weakly generalized closed set namely intuitionistic fuzzy rwT1/2 ...

After the introduction of the concept of a fuzzy set by Zadeh, several researches were conducted on the generalizations of the concept of a fuzzy set. The idea of intuitionistic fuzzy set is due to Atanassov [1], [2], [3] and recently Çoker [4] has defined the concept of intuitionistic fuzzy topological space which generalizes the concept of fuzzy topological space introduced by Chang [5]. Heil...

This paper is devoted to the study of intuitionistic fuzzy topological spaces. In this paper an intuitionistic fuzzy generalized pre-closed sets and an intuitionistic fuzzy generalized pre-open sets are introduced. Some of its properties are studied. Also we have provided some applications of intuitionistic fuzzy generalized pre-closed sets namely intuitionistic fuzzy pT1/2 space and intuitioni...

The concept of induced fuzzy topological space, introduced by Weiss [J. Math. Anal. Appl. 50(1975), 142-150], was defined with the notion of a lower semi-continuous function. The aim of this paper is to introduce and study the concepts of induced fuzzy supra-topological spaces and s-lower β-continuous functions. s-Lower β-continuous functions turn out to be the natural tool for studying the ind...

Based on a complete Heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a Cartesian-closed category, calledthe category of $L-$ordered fuzzifying convergence spaces, in whichthe category of $L-$fuzzifying topological spaces can be embedded.In addition, two new categories are introduced, which are called the...

Topological relationships between spatio-temporal objects are the most fundamental elements in spatio-temporal database systems, GIS, and image database systems. The research issue of modeling topological relationships has increasingly attracted attention, especially for querying of spatio-temporal objects and reasoning of topological relationships. Currently, topological relationship operating...

In recent years, formalization and reasoning of topological relations have become a hot topic as a means to generate knowledge about the relations between spatial objects at the conceptual and geometrical levels. These mechanisms have been widely used in spatial data query, spatial data mining, evaluation of equivalence and similarity in a spatial scene, as well as for consistency assessment of...