Following the ideas of the axiomatic characterization of the Choquet integral due to [D. Schmeidler, Integral representation without additivity, Proc. Amer. Math. Soc. 97 (1986) 255–261] and of the Sugeno integral given in [J.-L. Marichal, An axiomatic approach of the discrete Sugeno integral as a tool to aggregate interacting criteria in a qualitative framework, IEEE Trans. Fuzzy Syst. 9 (2001...

Jang, Kim and Kwon introduced a multi-valued Choquet integral for multifunctions with respect to real fuzzy measures and Zhang, Guo and Liu established for this kind of integral some convergence theorems. The aim of this paper is to present another type of set-valued Choquet integral, called by us the Aumann-Choquet integral, for non-negative measurable functions with respect to multisubmeasure...

Due to limitations of classical weighted average aggregation operators, there is an increase usage of fuzzy integrals, like the Sugeno and Choquet integrals, as alternative aggregation operators. However, their applicability has been threatened by the crux of determining the fuzzy measures in real problems. One way to determine these measures is by using learning data and optimizing the paramet...

Fuzzy measures and integrals have been used in multiple applications in the area of information fusion. They can be used to aggregate information when information sources are not independent. Fuzzy measures are used to represent our background knowledge on the information sources. In particular, they can be used to model the dependencies between the variables. One of the applications of Choquet...

In this paper, some properties of the monotone set-valued function defined by the set-valued Choquet integral are discussed. It is shown that several important structural characteristics of the original set function, such as null-additivity, strong order continuity, property(S) and pseudometric generating property, etc., are preserved by the new set-valued function. It is also shown that integr...

A new inequality for the universal integral on abstract spaces is obtained in a rather general form. As two corollaries, Minkowski’s and Chebyshev’s type inequalities for the universal integral are obtained. The main results of this paper generalize some previous results obtained for special fuzzy integrals, e.g., Choquet and Sugeno integrals. Furthermore, related inequalities for seminormed in...