Fuzzy Extension of Crisp Metric by Means of Fuzzy Equivalence Relation

Abstract

We develop an alternative approach to the fuzzy metric concept, which we obtain by fuzzy extension of a crisp metric d on a set X by means of a fuzzy equivalence relation E on the set IR+. We call it an E-d metric and study its properties and relations with “classical” fuzzy metrics. Our special interest is in the topologies and fuzzy topologies induced by E-d metrics.

Keywords

• <i>E</i>-<i>d</i>-metric
• fuzzy metric
• fuzzy equivalence relation
• extensional fuzzy set
• topology