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On the regularity of the fuzzy measure on metric fuzzy measure spaces. (English) Zbl 0844.28009
Summary: In this paper, the concept of regular fuzzy measure on metric spaces is introduced, some of its properties are discussed and Lusin’s theorem is shown. In addition, a condition for which a uniformly autocontinuous set function is a fuzzy measure is given.

28E10Fuzzy measure theory
Full Text: DOI
[1] Parthasarathy, K. R.: Probability measures on metric spaces. (1967) · Zbl 0153.19101
[2] Sugeno, M.: Theory of fuzzy integrals and its applications. Doctoral thesis (1974)
[3] Zhenyuan, Wang: The autocontinuity of set function and the fuzzy integral. J. math. Anal. appl. 99, 195-218 (1984) · Zbl 0581.28003
[4] Zhenyuan, Wang: Asymptotic structural characteristics of fuzzy measure and their applications. Fuzzy sets and systems 16, 277-290 (1985) · Zbl 0593.28007
[5] Zhenyuan, Wang: Null-additivity and autocontinuity of a fuzzy measure. Fuzzy sets and systems 45, 223-226 (1992) · Zbl 0751.28010