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- W4307287683 abstract "In this paper, we are focus on the family of all normal, upper semicontinuous with compact support fuzzy sets Fp(X) on a metric space (X,d) equipped with the dp-metric. We also consider the family, denoted by Fp⁎(X), of all normal upper semicontinuous fuzzy sets for which is possible to define a dp-metric. We prove the following results: Fp⁎(X) is separable if and only if X is separable. Fp⁎(X) is complete if and only if X is complete. We show that Fp(X) is complete if and only if X is compact. If Fp(X) is locally compact, then X is compact." @default.
- W4307287683 created "2022-10-31" @default.
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- W4307287683 date "2022-12-01" @default.
- W4307287683 modified "2023-09-27" @default.
- W4307287683 title "Some properties of the d-metrics on fuzzy sets" @default.
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- W4307287683 doi "https://doi.org/10.1016/j.topol.2022.108323" @default.
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