Journal of Advanced Computational Intelligence and Intelligent Informatics
Online ISSN : 1883-8014
Print ISSN : 1343-0130
ISSN-L : 1883-8014
Regular Papers
Fuzzy Multisets in Granular Hierarchical Structures Generated from Free Monoids
Tetsuya MuraiSadaaki MiyamotoMasahiro InuiguchiYasuo KudoSeiki Akama
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JOURNAL OPEN ACCESS

2015 Volume 19 Issue 1 Pages 43-50

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Abstract

Fuzzy multisets defined by Yager take multisets on interval (0,1] as grades of membership. As Miyamoto later pointed out, the fuzzy multiset operations originally defined by Yager are not compatible with those of fuzzy sets as special cases. Miyamoto proposed different definitions for fuzzy multiset operations. This paper focuses on the two definitions of fuzzy multiset operations, one by Yager and the other by Miyamoto. It examines their differences in the framework of granular hierarchical structures generated from the free monoids as proposed in our previous papers. In order to define basic order between multisets on interval (0,1], Yager uses the natural order on the range ℕ, the set of natural numbers, whereas Miyamoto newly introduces an order generated from both domain (0,1] and range ℕ through the notion of cuts.

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