Fuzzy properties in fuzzy convergence spaces

Gunther Jäger

doi:10.1155/s0161171202007664

Abstract

Based on the concept of limit of prefilters and residual implication, several notions in fuzzy topology are fuzzyfied in the sense that, for each notion, the degree to which it is fulfilled is considered. We establish therefore theories of degrees of compactness and relative compactness, of closedness, and of continuity. The resulting theory generalizes the corresponding “crisp” theory in the realm of fuzzy convergence spaces and fuzzy topology.

Highlights

In most papers and contributions to the theory of [0, 1]-topological spaces, the considered properties are viewed in a crisp way, that is, the properties either hold or fail
In [17], Šostak developed a theory of compactness degrees and connectedness degrees in [0, 1]-fuzzy topological spaces, and developed, in [18], a theory of degrees of precompactness and completeness in the so-called Hutton fuzzy uniform spaces
These latter theories are related to the present work as they are explicitly based on a generalized inclusion

Summary

GUNTHER JÄGER

Based on the concept of limit of prefilters and residual implication, several notions in fuzzy topology are fuzzyfied in the sense that, for each notion, the degree to which it is fulfilled is considered. We establish theories of degrees of compactness and relative compactness, of closedness, and of continuity. The resulting theory generalizes the corresponding “crisp” theory in the realm of fuzzy convergence spaces and fuzzy topology. 2000 Mathematics Subject Classification: 54A20, 54A40, 54C05, 54D30

Introduction

Conclusions