On conditions under which some generalized Sugeno integrals coincide: a solution to Dubois’ problem. (English) Zbl 1382.28014

Boczek, Michał; Kaluszka, Marek

Fuzzy Sets Syst. 326, 81-88 (2017).

Summary: In the paper, we characterize the class of all pairs of fuzzy implications and dual fuzzy implications such that the q-integral and q-cointegral coincide. This gives a solution to the problem posed by Didier Dubois during the conference FSTA 2016, the 13th International Conference on Fuzzy Set Theory and Applications. As a corollary, we obtain necessary and sufficient conditions under which the seminormed fuzzy integral and the semiconormed fuzzy integral are equal for all measurable functions.

MSC:

28E10	Fuzzy measure theory
26E50	Fuzzy real analysis

Keywords:

capacity; Sugeno integral; fuzzy implication; semicopula; q-integral; q-cointegral; seminormed fuzzy integral; semiconormed fuzzy integral

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