6533b86cfe1ef96bd12c8220

RESEARCH PRODUCT

On t-Conorm Based Fuzzy (Pseudo)metrics

Oscar ValeroAlexander ŠOstakJuan-josé MiñanaOlga Grigorenko

subject

Theoretical computer scienceLogicComputer scienceMathematics::General MathematicsCB-fuzzy (pseudo)metric02 engineering and technology01 natural sciencesFuzzy logic0202 electrical engineering electronic engineering information engineeringCB-fuzzy (pseudo)metric; archimedian t-(co)norms; hamacher t-(co)norm; modular; modular metric; intuinionistic fuzzy metricsmodular0101 mathematicsMathematical PhysicsAlgebra and Number Theoryintuinionistic fuzzy metricslcsh:Mathematicslcsh:QA1-939010101 applied mathematicsNorm (mathematics)hamacher t-(co)normmodular metric020201 artificial intelligence & image processingGeometry and TopologyComputingMethodologies_GENERALarchimedian t-(co)normsAnalysis

description

We present an alternative approach to the concept of a fuzzy (pseudo)metric using t-conorms instead of t-norms and call them t-conorm based fuzzy (pseudo)metrics or just CB-fuzzy (pseudo)metrics. We develop the basics of the theory of CB-fuzzy (pseudo)metrics and compare them with “classic” fuzzy (pseudo)metrics. A method for construction CB-fuzzy (pseudo)metrics from ordinary metrics is elaborated and topology induced by CB-fuzzy (pseudo)metrics is studied. We establish interrelations between CB-fuzzy metrics and modulars, and in the process of this study, a particular role of Hamacher t-(co)norm in the theory of (CB)-fuzzy metrics is revealed. Finally, an intuitionistic version of a CB-fuzzy metric is introduced and applied in order to emphasize the roles of t-norms and a t-conorm in this context.

yearjournalcountryeditionlanguage
2020-07-08Axioms
10.3390/axioms9030078https://www.mdpi.com/2075-1680/9/3/78