| Summary: | We present an alternative approach to the concept of a fuzzy (pseudo)metric using <i>t</i>-conorms instead of <i>t</i>-norms and call them <i>t</i>-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 <i>t</i>-(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 <i>t</i>-norms and a <i>t</i>-conorm in this context.
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