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Keywords = CB-fuzzy (pseudo)metric

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20 pages, 360 KB  
Article
On t-Conorm Based Fuzzy (Pseudo)metrics
by Olga Grigorenko, Juan Jose Miñana, Alexander Šostak and Oscar Valero
Axioms 2020, 9(3), 78; https://doi.org/10.3390/axioms9030078 - 8 Jul 2020
Cited by 15 | Viewed by 3201
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Fuzzy Set Theory and Applications)
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