Fuzzy Multisets and Their Generalizations

Fuzzy multisets with infinite membership sequences and their generalization using set-valued memberships are considered. Two metric spaces of the infinite fuzzy multisets are defined in terms of cardinality. One is the completion of fuzzy multisets of finite membership sequences; the other is derived from operations among fuzzy multisets and realvalued multisets. Theoretical properties of these infinite fuzzy multisets are discussed.

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