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Fuzzy distances. (English) Zbl 1249.54013

Summary: In the paper three different ways of constructing distances between vaguely described objects are shown: a generalization of the classic distance between subsets of a metric space, a distance between membership functions of fuzzy sets and a fuzzy metric introduced by generalizing a metric space to a fuzzy-metric space. Fuzzy metric spaces defined by Zadeh’s extension principle, particularly to \(\mathbb {R}^n\), are dealt with in detail.

MSC:

54A40 Fuzzy topology
54E35 Metric spaces, metrizability
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References:

[1] Bednář J.: The fuzzy rational database system FSearch 2. 0. Proc. 6th Internat. Conference on Soft Computing MENDEL, Brno 2000, pp. 232-237
[2] Bednář J.: Properties of fuzzy metrics on \(R^{n}\). Proc. East West Fuzzy Colloquium 2002 and 10th Zittau Fuzzy Colloquium, Zittau 2002, pp. 2-6
[3] Gerla G., Volpe R.: The definition of distance and diameter in fuzzy set theory. Stutia Univ. Babes-Bolyai Math. 31 (1986), 21-26 · Zbl 0594.54004
[4] Kaleva O., Seikkala S.: On fuzzy metric spaces. Fuzzy Sets and Systems 12 (1984), 215-229 · Zbl 0558.54003 · doi:10.1016/0165-0114(84)90069-1
[5] Klir G., Yuan B.: Fuzzy Set and Fuzzy Logic: Theory and Applications. Prentice Hall, Englewood Cliffs, NJ 1995 · Zbl 0915.03001
[6] Mareš M.: Computation over Fuzzy Quantities. CRC Press, Boca Raton 1994 · Zbl 0859.94035
[7] Osman A.: Fuzzy metric spaces and fixed fuzzy set theorem. Bull. Malaysian Math. Soc. 6 (1983), 1, 1-4 · Zbl 0541.54063
[8] Rudin W.: Real and Complex Analysis. McGraw-Hill, New York 1984 · Zbl 1038.00002
[9] Szmidt E., Kacprzyk J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems 114 (2000), 505-518 · Zbl 0961.03050 · doi:10.1016/S0165-0114(98)00244-9
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