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Fuzzy number-valued fuzzy measure and fuzzy number-valued fuzzy integral on the fuzzy set. (English) Zbl 0782.28017
Summary: Some new concepts – the fuzzy number-valued fuzzy measure, autocontinuity and null-additivity of fuzzy number-valued fuzzy measures on the fuzzy $$\sigma$$-algebra, and the fuzzy number-valued fuzzy integral on the fuzzy set – are introduced. Some properties of fuzzy number- valued fuzzy integrals and some convergence theorems for sequences of fuzzy number-valued fuzzy integrals on a fuzzy set are discussed.

MSC:
 2.8e+11 Fuzzy measure theory
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References:
 [1] Zhenyuan, Wang, The autocontinuity of set function and fuzzy integral, J. math. anal. appl., 99, 195-218, (1984) · Zbl 0581.28003 [2] Guangquan, Zhang, Fuzzy distance and limit of fuzzy numbers, Busefal, 33, 19-30, (1987) · Zbl 0685.54002 [3] Guangquan, Zhang, Fuzzy limit theory of fuzzy numbers, () · Zbl 0685.54002 [4] Guangquan, Zhang, Fuzzy continuous function and its properties, Fuzzy sets and systems, 43, 159-171, (1991) · Zbl 0735.26013 [5] Guangquan, Zhang, FSC-fuzzy measure and fuzzy integral on the fuzzy set, J. hebei university, 4, 11-23, (1988), (in Chinese) [6] Wenxiu, Zhang, Elements of fuzzy mathematics, (1984), Xian Jiaotong University, (in Chinese) · Zbl 0599.28010 [7] Sugeno, M., Theory of fuzzy integrals and its applications, () · Zbl 0316.60005 [8] Zadeh, L.A., Fuzzy sets, Inform. and control, 8, 338-353, (1965) · Zbl 0139.24606
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