## 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.

### MSC:

 2.8e+11 Fuzzy measure theory 2.6e+51 Fuzzy real analysis
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### References:

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