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\(L\)-metric on the space of \(L\)-fuzzy numbers. (English) Zbl 1464.54011

Summary: In this article, a natural \(L\)-topology is constructed on the set of \(L\)-fuzzy numbers, which is called the standard \(L\)-topology. It is proved that the standard \(L\)-topology can be induced by an \(L\)-metric. The space of trapezoidal fuzzy numbers can be regarded as a subspace of the space of \(L\)-fuzzy numbers. An \(L\)-metric on the set of trapezoidal fuzzy numbers is presented.

MSC:

54A40 Fuzzy topology
54E35 Metric spaces, metrizability
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