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

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.


28E10 Fuzzy measure theory
26E50 Fuzzy real analysis
Full Text: DOI


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