Keywords: Fuzzy measure Sugeno integral Choquet integral Stolarsky's inequality a b s t r a c t Recently Flores-Franulič, Román-Flores and Chalco-Cano proved the Stolarsky type inequality for Sugeno integral with respect to the Lebesgue measure k. The present paper is devoted to generalize this result by relaxing some of its requirements. Moreover, Stolar-sky inequality for Choquet integral is ...

In this paper we consider a multicriteria aggregation model where local utility functions of different sorts are aggregated using Sugeno integrals, and which we refer to as Sugeno utility functions. We propose a general approach to study such functions via the notion of pseudoSugeno integral (or, equivalently, pseudo-polynomial function), which naturally generalizes that of Sugeno integral, and...

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...

We present a model allowing to aggregate decision criteria when the available information is of a qualitative nature. The use of the Sugeno integral as an aggregation function is justified by an axiomatic approach. It is also shown that the mutual preferential independence of criteria reduces the Sugeno integral to a dictatorial aggregation.

Fuzzy integrals are commonly used as aggregation operators. In this paper we present new composite models based on fuzzy integrals with several t-conorms. These models permit to further increase the computational power of the previous models. Basic properties of new composite models are studied. In particular, it is shown that for composite models, the only meaningful case is when not all the t...

Minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. Also related inequalities to Minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. Several examples are given to illustrate the validity of theorems. Some results on Chebyshev and Minkowski type inequalities are obtained.

Comonotone maxitive idempotent aggregation functions on [0, 1] are characterized and the extended Sugeno integral is introduced. Also the relationship of Sugeno integral and the extended Sugeno integral is clarified. Finally, extended weighted maxima on [0, 1] are discussed.

We show that the Choquet integral is the unique linear interpolator between vertices of the [0, 1] hypercube, using the least possible number of vertices. Related results by Lovász and Singer are discussed, as well as other interpolations. We show that the Choquet integral for bi-capacities can be also casted into this framework. Lastly, we discuss the case of Sugeno integral.

In this note, we consider a similar type of Gauss inequality for fuzzy integrals. More precisely, we show that the inequality x(S) ∫ ∞

Fuzzy measures were introduced by M Sugeno in in order to express a grade of fuzziness in the same way that probability measures express a grade of random ness The Sugeno fuzzy integrals are the functionals with monotonicity de ned by using fuzzy measures Later on Murofushi and Sugeno proposed another type of fuzzy integral the Choquet integral based on the Capacity Theory developed by G Choque...