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2016•Iranian journal of fuzzy systemsRequires access

ON METRIC SPACES INDUCED BY FUZZY METRIC SPACES

Dong Qiu, Rongwen Dong, Haolin Li

Open publisher page 5 citations

Abstract

For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm,  we present a method to construct a metric on a  fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space.  Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some problems for fuzzy metric spaces  in the  literature, which are shown by   examples in this paper.

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What this paper is about

For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm,  we present a method to construct a metric on a  fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space.  Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some problems for fuzzy metric spaces  in the  literature, which are shown by   examples in this paper.

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Available abstract

For a class of fuzzy metric spaces (in the sense of George and Veeramani) with an H-type t-norm,  we present a method to construct a metric on a  fuzzy metric space. The induced metric space shares many important properties with the given fuzzy metric space.  Specifically, they generate the same topology, and have the same completeness. Our results can give the constructive proofs to some problems for fuzzy metric spaces  in the  literature, which are shown by   examples in this paper.

Key concepts: T-norm, Injective metric space, Convex metric space, Mathematics, Intrinsic metric, Equivalence of metrics, Metric space, Metric differential

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