Fuzzy Metrics in Terms of Fuzzy Relations

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

Mathematics, 2023, vol. 11, issue 16, 1-13

Abstract: In this paper, we study the concept of fuzzy metrics from the perspective of fuzzy relations. Specifically, we analyze the commonly used definitions of fuzzy metrics. We begin by noting that crisp metrics can be uniquely characterized by linear order relations. Further, we explore the criteria that crisp relations must satisfy in order to determine a crisp metric. Subsequently, we extend these conditions to obtain a fuzzy metric and investigate the additional axioms involved. Additionally, we introduce the definition of an extensional fuzzy metric or E - d -metric, which is a fuzzification of the expression d ( x , y ) = t . Thus, we examine fuzzy metrics from both the linear order and from the equivalence relation perspectives, where one argument is a value d ( x , y ) and the other is a number within the range [ 0 , + ∞ ) .

Keywords: metric; order relation; fuzzy metric; fuzzy relation; fuzzy order; fuzzy equivalence; extensional fuzzy metric (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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