On t-Conorm Based Fuzzy (Pseudo)metrics
| Autor: | Oscar Valero, Alexander Šostak, Juan-José Miñana, Olga Grigorenko |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Theoretical computer science
Logic Computer science Mathematics::General Mathematics CB-fuzzy (pseudo)metric 02 engineering and technology 01 natural sciences Fuzzy logic 0202 electrical engineering electronic engineering information engineering archimedian t-(co)norms hamacher t-(co)norm modular modular metric intuinionistic fuzzy metrics 0101 mathematics Mathematical Physics Algebra and Number Theory lcsh:Mathematics lcsh:QA1-939 010101 applied mathematics Norm (mathematics) 020201 artificial intelligence & image processing Geometry and Topology ComputingMethodologies_GENERAL Analysis |
| Zdroj: | Axioms, Vol 9, Iss 78, p 78 (2020) Axioms; Volume 9; Issue 3; Pages: 78 |
| ISSN: | 2075-1680 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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