Fuzzy Multisets in Granular Hierarchical Structures Generated from Free Monoids | Zendy

Tetsuya Murai | Zendy; Sadaaki Miyamoto | Zendy; Masahiro Inuiguchi | Zendy; Yasuo Kudo | Zendy; Seiki Akama | Zendy

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Fuzzy Multisets in Granular Hierarchical Structures Generated from Free Monoids

Author(s) -

Tetsuya Murai,

Sadaaki Miyamoto,

Masahiro Inuiguchi,

Yasuo Kudo,

Seiki Akama

Publication year - 2015

Publication title -

journal of advanced computational intelligence and intelligent informatics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.172

H-Index - 20

eISSN - 1343-0130

pISSN - 1883-8014

DOI - 10.20965/jaciii.2015.p0043

Subject(s) - multiset , fuzzy logic , range (aeronautics) , mathematics , order (exchange) , fuzzy set , interval (graph theory) , domain (mathematical analysis) , set (abstract data type) , computer science , discrete mathematics , artificial intelligence , combinatorics , mathematical analysis , materials science , finance , economics , composite material , programming language

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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