Abstract In this paper, we present the Sugeno integral of Hermite–Hadamard inequality for case quasi-arithmetically convex (q-ac) functions which acts as a generator all quasi-arithmetic means in frame work integral.

In this paper, we  present a version of Favard's inequality for special case and then generalize it for the Sugeno integral in fuzzy measure space $(X,Sigma,mu)$, where $mu$ is the Lebesgue measure. We consider two cases, when our function is concave and when is convex. In addition for illustration of theorems, several examples are given.

We study the filter design problem for Takagi-Sugeno fuzzy systems which are subject to norm-bounded uncertainties in each subsystem. As we know that the Takagi-Sugeno fuzzy linear systems can be used to represent smooth nonlinear systems, the studied plants can also be uncertain complex systems. We suppose to design a filter with the order of the original system which is also dependent on the ...

Considering the space of all non–negative measurable functions F(X,A) linked to a fixed measurable space (X,A), the Lebesgue integral can be seen as an additive, continuous from below functional L on F(X,A), related to a measure m : A → [0,∞] given by m(A) = L(1A). We introduce several other integrals which can be seen as special functionals on F(X,A). For example, the Choquet integral [7] is a...

In this paper further development of Chebyshev type inequalities for Sugeno integrals based on an aggregation function H and a scale transformation ϕ is given. Consequences for T-(S-)evaluators are established.

This paper presents a synthesis on the essential mathematical properties of Choquet and Sugeno integrals viewed as aggregation functions. Some axiomatic characterizations are presented. Subfamilies of the class of those integrals are also investigated.

We introduce a Choquet-Sugeno-like operator generalizing many operators for bounded nonnegative functions and monotone measures from the literature, e.g., Sugeno-like operator, Lovász Owen measure extensions, F-decomposition integral with respect to partition decomposition system, others. The new is based on concepts of dependence relation conditional aggregation operators, but it does not depe...