×

zbMATH — the first resource for mathematics

A theory of fuzzy measures: Representations, the Choquet integral, and null sets. (English) Zbl 0735.28015
Regardless the continuity, authors define the fuzzy measure as a nonnegative monotone set function on a measurable space. By using classical measures, a representation of fuzzy measures is shown in this paper. Furthermore, the authors give a necessary and sufficient condition that, for any given fuzzy measure, the Choquet integral is additive. Also, the authors generalize the concepts of null sets and ”a.e.” on fuzzy measure spaces.

MSC:
28E10 Fuzzy measure theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Choquet, G, Theory of capacities, Ann. inst. Fourier, 5, 131-295, (1955) · Zbl 0064.35101
[2] Höhle, U, A mathematical theory of uncertainty, (), 344-355
[3] Murofushi, T; Sugeno, M, An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure, Fuzzy sets and systems, 29, 201-227, (1989) · Zbl 0662.28015
[4] Sugeno, M, Theory of fuzzy integrals and its applications, () · Zbl 0316.60005
[5] Wang, Z, The autocontinuity of set function and the fuzzy integral, J. math. anal. appl., 99, 195-218, (1984) · Zbl 0581.28003
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.