It is known that a hierarchical decision structure consisting of multiple criteria can be modeled by a Choquet integral-based hierarchical network. With a given input–output dataset, the degree of importance of each criterion can be directly obtained from the corresponding connection weight after the network has been trained from samples. Since each output value or the synthetic evaluation of a...

The well known fuzzy measures, λ-measure and P-measure, have only one formulaic solution. A multivalent fuzzy measure with infinitely many solutions based on Pmeasure was proposed by our previous work, called completed L-measure. In this paper, a further improved fuzzy measure, called extensional completed L-measure, is proposed. This new fuzzy measure is proved that it is not only an extension...

In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions to represent a cardinal preferential information by the Choquet integral w.r.t. a 2-additive capacity. These conditions are based on some complex cycles called cyclones.

This paper studies some relationships between fuzzy relations, fuzzy graphs and fuzzy measure. It is shown that a fundamental theorem of Discrete Convex Analysis is derived from the theory of fuzzy measures and the Choquet integral.

At first, we consider nonnegative monotone interval-valued set functions and nonnegative measurable interval-valued functions. In this paper we investigate some properties and structural characteristics of the monotone interval-valued set function defined by an interval-valued Choquet integral.

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...

A new solution concept: acceptable payoffs in the core via coalition formation Katsushige Fujimoto Inequalities for Choquet integral with respect to a submodular non additive measure Yasuo Narukawa, Vicenç Torra

Our main goal is to extend the domain of a monotone measure to a class of intuitionistic fuzzy sets. The extension is made by using of the Choquet integral.

Given a real valued random variable Θ we consider Borel measures μ on B(R), which satisfy the inequality μ(B) ≥ Eμ(B−Θ) (B ∈ B(R)) (or the integral inequality μ(B) ≥ R∞ −∞ μ(B−h)γ(dh)). We apply the Choquet theorem to obtain an integral representation of measures μ satisfying this inequality. We give integral representations of these measures in the particular cases of the random variable Θ.