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:i)Fp⁎(X) is separable if and only if X is separable.ii)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.
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