Abstract
Two generalizations of multisets are considered. First, a class of fuzzy multisets which have an infinite membership set for an element of the universe and finite cardinality is introduced. It is shown that the sum, union, intersection, average as well as most t-norm and conorm operations for two sets in this class except the drastic sum keep the property of the finite cardinality of the derived set. Second, the membership sequence is generalized to a closed set on the plane whereby both infinite fuzzy multisets and real-valued multisets are discussed in a unified framework.
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Miyamoto, S. (2003). Two Generalizations of Multisets. In: Inuiguchi, M., Hirano, S., Tsumoto, S. (eds) Rough Set Theory and Granular Computing. Studies in Fuzziness and Soft Computing, vol 125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36473-3_6
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DOI: https://doi.org/10.1007/978-3-540-36473-3_6
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