Abstract
Fuzzymultisets with infinitemembership 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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References
W.D. Blizard, Multiset theory, Notre Dame Journal of Formal logic, Vol. 30, No. 1,pp. 36–66, 1989.
W.D. Blizard, Real-valued multisets and fuzzy sets, Fuzzy Sets and Systems,Vol. 33, pp. 77–97, 1989.
B. Li, W. Peizhang, L. Xihui, Fuzzy bags with set-valued statistics, Comput. Math.Applic., Vol. 15, pp. 811–818, 1988.
K.S. Kim and S. Miyamoto, Application of fuzzy multisets to fuzzy database systems,Proc. of 1996Asian Fuzzy Systems Symposium, Dec. 11–14, 1996, Kenting,Taiwan, R.O.C. pp. 115–120, 1996.
D.E. Knuth, The Art of Computer Programming, Vol.2 / Seminumerical Algorithms,Addison-Wesley, Reading, Massachusetts, 1969.
Z.-Q. Liu, S. Miyamoto (Eds.), Soft Computing and Human-Centered Machines,Springer, Tokyo, 2000.
Z. Manna and R. Waldinger, The Logical Basis for Computer Programming, Vol.1: Deductive Reasoning, Addison-Wesley, Reading, Massachusetts, 1985.
S. Miyamoto, Fuzzy multisets with infinite collections of memberships, Proc. ofthe 7th International Fuzzy Systems Association World Congress (IFSA’97), June25–30, 1997, Prague, Chech, Vol.1, pp.61–66, 1997.
S. Miyamoto, K.S. Kim, An image of fuzzy multisets by one variable function andits application, J. of Japan Society for Fuzzy Theory and Systems, Vol. 10, No. 1,pp. 157–167, 1998 (in Japanese).
S. Miyamoto, K.S. Kim, Multiset-valued images of fuzzy sets, Proceedings of theThird Asian Fuzzy Systems Symposium, June 18–21, 1998, Masan, Korea, pp.543–548.
S. Miyamoto, Rough sets and multisets in a model of information retrieval, inF. Crestani and G. Pasi, eds., Soft Computing in Information Retrieval: Techniquesand Applications, Springer, pp. 373–393, 2000.
Z. Pawlak, Rough Sets, Kluwer, Dordrecht, 1991.
A. Ramer, C.-C. Wang, Fuzzy multisets, Proc. of 1996Asian Fuzzy Systems Symposium,Dec. 11–14, 1996, Kenting, Taiwan, pp. 429–434.
A. Rebai, Canonical fuzzy bags and bag fuzzy measures as a basis for MADM withmixed non cardinal data, European J. of Operational Res., Vol. 78, pp. 34–48, 1994.
A. Rebai, J.-M. Martel, A fuzzy bag approach to choosing the “best” multiattributedpotential actions in a multiple judgement and non cardinal data context,Fuzzy Sets and Systems, Vol. 87, pp. 159–166, 1997.
R.R. Yager, On the theory of bags, Int. J. General Systems, Vol. 13, pp. 23–37,1986.
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Miyamoto, S. (2001). Fuzzy Multisets and Their Generalizations. In: Calude, C.S., PĂun, G., Rozenberg, G., Salomaa, A. (eds) Multiset Processing. WMC 2000. Lecture Notes in Computer Science, vol 2235. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45523-X_11
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DOI: https://doi.org/10.1007/3-540-45523-X_11
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