Fuzzy Multisets in Granular Hierarchical Structures Generated from Free Monoids
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Published:2015-01-20
Issue:1
Volume:19
Page:43-50
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ISSN:1883-8014
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Container-title:Journal of Advanced Computational Intelligence and Intelligent Informatics
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language:en
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Short-container-title:JACIII
Author:
Murai Tetsuya, ,Miyamoto Sadaaki,Inuiguchi Masahiro,Kudo Yasuo,Akama Seiki, , , ,
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 rangeN, the set of natural numbers, whereas Miyamoto newly introduces an order generated frombothdomain (0,1] and rangeNthrough the notion of cuts.
Publisher
Fuji Technology Press Ltd.
Subject
Artificial Intelligence,Computer Vision and Pattern Recognition,Human-Computer Interaction
Reference21 articles.
1. W. D. Blizard, “Multiset theory,” Notre Dame J. of Formal Logic Vol.30, pp. 36-66, 1989. 2. S. P. Jena, S. K. Ghosh, and B. K. Tripathy, “On the theory of bags and lists,” Information Sciences, Vol.132, pp. 241-254, 2001. 3. D. E. Knuth, “The Art of Computer Programming,” Vol.2, Addison-Wesley, Reading, Massachusetts, 1969. 4. D. Singh, A. M. Ibrahim, A. Bello, T. Yohanna, and J. N. Singh, “A systematization of fundamentals of multisets,” Lecturas Matemáticas, Vol.29, pp. 33-48, 2008. 5. C.-C. Chan, “Learning rules from very large databases using rough multisets,” Trans. on Rough Sets I, LNCS 3100, pp. 59-77, 2004.
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