Abstract
One of the most important topics of research in fuzzy sets is to get an appropriate notion of fuzzy metric space (FMS), in the paper we propose a new FMS–tripled fuzzy metric space (TFMS), which is a new generalization of George and Veeramani’s FMS. Then we present some related examples, topological properties, convergence of sequences, Cauchy sequence (CS) and completeness of the TFMS. Moreover, we introduce two kinds of notions of generalized fuzzy ψ-contractive (Fψ-C) mappings, and derive a fixed point theorem (FPT) on the mappings in the space.
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