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Supremum metric on the space of fuzzy sets and common fixed point theorems for fuzzy mappings. (English) Zbl 1151.54010
Let (X,d) be a metric space. Let 𝒞(X) be the collection of fuzzy sets μ, such that the α-cut of μ is a nonempty bounded closed set in X, and let d be the metric for 𝒞(X) where d is induced by the Hausdorff metric. The authors establish that if (X,d) is complete, then (𝒞(X)) is also a complete metric space. Some common fixed point theorems for fuzzy mappings are proved.
MSC:
54A40Fuzzy topology
54E35Metric spaces, metrizability
03E72Fuzzy set theory
54H25Fixed-point and coincidence theorems in topological spaces
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