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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.

MSC:

28E10 Fuzzy measure theory
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References:

[1] Parthasarathy, K. R., Probability Measures on Metric Spaces (1967), Academic Press: Academic Press New York · Zbl 0153.19101
[2] Sugeno, M., Theory of fuzzy integrals and its applications, (Doctoral Thesis (1974), Tokyo Institute of Technology) · Zbl 0316.60005
[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
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