On the convergence of sequences in fuzzy topological spaces

Abstract

Analogous to classical topology, the concept of fuzzy nets, in particular, fuzzy sequences and its convergence play a fundamental role in fuzzy topology. There are several different ways of defining fuzzy convergence. The present paper is based on the definition of convergence of fuzzy sequences in terms of quasi-coincidence and Qneighbourhoods. The study aims at investigating the convergence of fuzzy sequences in various fuzzy topological spaces. The nature of convergent sequences of fuzzy points in certain fuzzy topological spaces such as fuzzy indiscrete, fuzzy discrete, fuzzy co-finite etc. are studied. Characterization theorems for the convergence of fuzzy sequences in each space are obtained. Also, characterizations of fuzzy indiscrete topological space using convergence of fuzzy sequences are provided. The concepts of maximal limit, l-set, lm-set and fuzzy l-set of fuzzy sequences are introduced and their properties are explored.