Fuzzy Extension of Crisp Metric by Means of Fuzzy Equivalence Relation

Olga Grigorenko () and Alexander Šostak
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Olga Grigorenko: Institute of Mathematics and CS, University of Latvia, 1459 Riga, Latvia
Alexander Šostak: Institute of Mathematics and CS, University of Latvia, 1459 Riga, Latvia

Mathematics, 2022, vol. 10, issue 24, 1-15

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 I R + . 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: E - d -metric; fuzzy metric; fuzzy equivalence relation; extensional fuzzy set; topology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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