Axioms (Jul 2020)

On <i>t</i>-Conorm Based Fuzzy (Pseudo)metrics

  • Olga Grigorenko,
  • Juan Jose Miñana,
  • Alexander Šostak,
  • Oscar Valero

DOI
https://doi.org/10.3390/axioms9030078
Journal volume & issue
Vol. 9, no. 3
p. 78

Abstract

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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.

Keywords