Estimations, convergences and comparisons on fuzzy integrals of Sugeno, Choquet and Gould type

The subject of this paper concerns fuzzy integrals and fuzzy convergences. The first topic consists of presenting some relationships among different types of integrals of multi-functions relative to a fuzzy measure such as the strong and the weak Sugeno type integrals, the Aumann-Gould integral and the Dunford integral. A new estimation result on the strong integral is also established. Secondly, we present new connections among different types of integrals of real functions relative to a fuzzy measure such as the Gould integral, the Birkhoff integral, the Choquet integral and the non-linear integrals introduced in [30], [31]. Then we focus on establishing new links among different types of fuzzy convergences for sequences of multifunctions with respect to a fuzzy (or a non-additive) measure such as almost everywhere convergence, pseudo-almost everywhere convergence, almost uniformly convergence, pseudo-almost uniformly convergence, mean convergence and convergence in measure. In the end, we emphasize some applications of fuzzy integrals and fuzzy convergences, for example, in accident rate predictions, in subjective evaluations etc.