×

zbMATH — the first resource for mathematics

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:
28E10 Fuzzy measure theory
PDF BibTeX XML Cite
Full Text: DOI
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.