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...

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...

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.

This paper shows the detection of textures by analysing the image by stochastic properties. Different parts of the composed stochastic properties are fused by a decision directed method. The stochastic is mapped on a fuzzy measure and a fuzzy function. The fusion of the so represented stochastic information is achieved by the fuzzy integral. The result of the fuzzy integral is used for a new fu...

We consider a fixed probability μ. For any λ ∈ (−1,∞), we denote by m(λ, μ) the λ-Sugeno measure generated by μ. For a fixed measurable set A, the continuity of the map λ 7−→ ∫ A fdm(λ, μ) is proved, where the integral is either Choquet or Sugeno. The asymptotic (marginal) cases λ = −1 and λ =∞ are studied too. Finally, some concrete computations illustrate the previous theory.

We consider a fixed probability µ. For any () 1, λ ∈ − ∞ , we denote by () , m λ µ the λ-Sugeno measure generated by µ. For a fixed measurable set A, the continuity of the map () , A fdm λ λ µ ∫ ֏ is proved, where the integral is either Choquet or Sugeno. The asymptotic (marginal) cases 1 λ = − and λ = ∞ are studied too. Finally, some concrete computations illustrate the previous theory.

We prove two kinds of Lyapunov type inequalities for pseudo-integrals. One discusses pseudo-integrals where pseudo-operations are given by a monotone and continuous function g. The other one focuses on the pseudo-integrals based on a semiring 0; 1 ½ Š; sup; ð Þ , where the pseudo-multiplication is generated. Some examples are given to illustrate the validity of these inequalities. As a generali...

Aggregation refers to the process of combining numerical values x1, . . . , xm into a single one M (x1, . . . , xm), so that the final result of aggregation takes into account all the individual values. In decision making, values to be aggregated are typically preference or satisfaction degrees and thus belong to the unit interval [0, 1]. This paper aims at investigating the Sugeno integral whi...