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Fuzzy metric and convergences based on the symmetric difference

✍ Scribed by Congxin Wu; Fachao Li

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
123 KB
Volume
108
Category
Article
ISSN
0165-0114

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✦ Synopsis

In this paper, by applying the Lebesgue's measure on the symmetric di erence of sets, we introduce the notions of the symmetric di erence metric d and p-mean symmetric di erence metric d p in order to measure the di erence between fuzzy numbers. The concept of the platform type of fuzzy number (p-fuzzy number) is introduced, and we show that d and d p are zero if and only if two fuzzy numbers are equal or have the same p-fuzzy numbers. Further, the relations between d and the uniform Hausdor metric DH (cf. , d p and Dp (cf. are discussed. For the non-p-fuzzy numbers, the equivalences of the metric convergences on d and DH, d p and Dp are provided.

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