An axiomatization of the concept of entropy of a discrete Choquet capacity is given. It is based on three axioms: the symmetry property, a boundary condition for which the entropy reduces to the classical Shannon entropy, and a generalized version of the well-known recursivity property. This entropy, recently introduced to extend the Shannon entropy to nonadditive measures, fulfills several pro...

We propose the concepts of superadditive and of subadditive transformations of aggregation functions acting on non-negative reals, in particular of integrals with respect to monotone measures. We discuss special properties of the proposed transforms and links between some distinguished integrals. Superadditive transformation of the Choquet integral, as well as of the Shilkret integral, is shown...

Data envelopment analysis (DEA) is a non-parametric method for measuring the efficiencies of decision-making units (DMUs) by using set inputs and outputs. However, traditional DEA models always assume that or outputs are independent each other, which unrealistic in practical problems. To reflect interactions between outputs, Choquet integral employed models. The usually used to find some specif...

We study a generalization of necessity functions to MV-algebras. In particular, we are going to study belief functions whose associated mass assignments have nested focal elements. Since this class of belief functions coincides with necessity functions on Boolean algebras, we will call them generalized necessity functions. Using geometrical and combinatorial techniques we provide several charac...

The concept of universal integral, recently proposed and axiomatized, encompasses several integrals, including the Choquet, Shilkret and Sugeno integrals. In this paper we present two new axiomatizations of universal integrals on the scale 1⁄20;1 . In the first characterization, we look at universal integrals on the scale 1⁄20;1 as families of aggregation functions F satisfying some desired pro...

Recently, the TODIM$^1$(an acronym in Portuguese of interactive and multi-criteria decision making) method has attracted increasing attention and many researchers have extended it to deal with multiple attribute decision making (MADM) problems under different situations. However, none of them can be used to handle MADM problems with positive, independent, and negative interactions among attribu...

Abstract Fuzzy integrals are common concepts which used to aggregate input values in practical applications. Aggregation of inputs using fuzzy opens up numerous possibilities for modeling interaction, redundancy, and synergy inputs. However, need a measure start this aggregation process. This situation pushes us into the identification process becomes difficult due monotony condition exponentia...