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Non-additive measure and integral, basic concepts and their role for applications. (English) Zbl 0968.28009
Grabisch, Michel (ed.) et al., Fuzzy measures and integrals. Theory and applications. Heidelberg: Physica-Verlag. Stud. Fuzziness Soft Comput. 40, 42-69 (2000).
The paper gives an interesting overview about the main mathematical concepts and ideas in the non-additive theory of measure and integral. The intention of the author is to give a flavor of the theory in emphasizing the basic concepts and their role for applications. For the sake of simplicity and in order to minimize technicalities the author mostly restricts to finite basic sets, i.e., to the discrete setting. For a presentation of the theory in a much more general setting, see D. Denneberg [“Non-additive measure and integral” (1994; Zbl 0826.28002)].
For the entire collection see [Zbl 0935.00014].
Reviewer: Hans Weber (Udine)

28E10 Fuzzy measure theory
28A12 Contents, measures, outer measures, capacities