Fuzzy mathematics and its applications

Abstract

The thesis deals mainly with fuzzy topological concepts fuzzy filters newlineand applications of fuzzy mathematics newlineIn the thesis the notions of fuzzily closed subset nearly fuzzy newlineRegularity fuzzy regularity of a fuzzy topological space and the notion of newlinesemi Hausdorffness on fuzzy filters have been introduced and their properties newlinehave been studied A new concept of strongly fuzzily closed subset of a newlineproduct fuzzy topological space is introduced and the equivalent condition of newlinenearly fuzzy Hausdorffness has been studied The necessary and sufficient newlinecondition for a fuzzy topological space to be a nearly fuzzy regular space has newlinebeen discussed It has been proved that the arbitrary product of nearly fuzzy newlineregular spaces is nearly fuzzy regular space But in the case of fuzzy newlineregularity only the finite product of fuzzy regular spaces is a fuzzy regular newlinespace It is shown that the arbitrary product of fuzzy regular spaces need not newlinebe a fuzzy regular space The relations between the existing definitions and newlinenew notions have been discussed newline newline