The Choquet integral with respect to a level dependent capacity

Choquet-like integrals with respect to level-dependent capacities and φ-ordinal sums of aggregation function

“…A capacity v : A → [0, 1] can be regarded as a weighting function assigning a weight to a group of criteria A ∈ A. The idea of such weight being dependent on the level of criteria satisfaction degrees to be aggregated led Greco et al [4] to the introduction of level-dependent capacities. …”

“…A function f ∈ F A , such that for a given level-dependent capacity M the function h M,f is Lebesgue integrable, is called an M -integrable function. [4]) Let M be a fixed level-dependent capacity and let f ∈ F A be M -integrable. Then the Choquet integral of f with respect to M (with the notation Ch M (f )) is defined by…”

“…From among several generalizations of the Choquet integral, we will consider the concept of Choquet-like integrals [5] and the concept of the Choquet integral with respect to level-dependent capacities [4]. The main aim of this paper is the introduction of Choquet-like integrals with respect to level-dependent capacities and the study of representation of these integrals by means of special ordinal sums introduced in [6], see also [3].…”

Sandor Type Fuzzy Inequality Based on the (s,m)-Convex Function in the Second Sense

“…Because of the special integral operator of the Sugeno integral, it is limited in many practical problems. To overcome this shortcoming, many scholars have replaced the Sugeno integral in large or small operations with new operators, and they have proposed various types of fuzzy integrals, such as the Shilkret integral [10], the bipolar level Choquet integral [11], the level-dependent Sugeno integral [12], etc. In recent years, some famous integral inequalities have been generalized to fuzzy integrals (cf.…”

Indicators for the characterization of discrete Choquet integrals

“…Over the last few years, the Choquet integral has received much attention from researchers, and this has generated new extensions and generalizations of this class of integral. For instance, Greco et al [12] proposed an extension of Choquet integrals in which the capacities depend on the values to be aggregated. Similarly, Yager [39] presented new induced aggregation operators inspired by Choquet integrals and Xu [34] introduced some intuitionistic fuzzy aggregation functions also based on the Choquet integral.…”