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Quantitative approximation by shift invariant multivariate sublinear-Choquet operators

Anastassiou G. A.

Journal of Applied Analysis

2018

Vol. 24, nr 2

115--126

A very general multivariate positive sublinear Choquet integral type operator is given through a convolution-like iteration of another multivariate general positive sublinear operator with a multivariate scaling type function. For it, sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates. Furthermore, two examples of very general multivariate specialized operators are presented fulfilling all the above properties; the higher order of multivariate approximation of these operators is also studied.

Choquet integral calculus on a continuous support and its applications

Ridaoui M., Grabisch M.

Operations Research and Decisions

2016

Vol. 26, No. 1

73--93

The results of the calculation of the Choquet integral of a monotone function on the nonnegative real line have been described. Next, the authors prepresented Choquet integral of nonmonotone functions, by constructing monotone functions from nonmonotone ones by using the increasing or decreasing rearrangement of a nonmonotone function. Finally, this paper considers some applications of these results to the continuous agregation operator OWA, and to the representation of risk measures by Choquet integral.

Preorder Information Based Attributes’ Weights Learning in Multi-attribute Decision Making

Wang B., Liang J., Qian Y.

Fundamenta Informaticae

2014

Vol. 132, nr 3

331--347

Choquet integral, as an adequate aggregation operator, extends the weighted mean operator by considering interactions among attributes. Choquet integral has been widely used in many real multi-attribute decision making. Weights (fuzzy measures) of attribute sets directly affect the decision results in multi-attribute decision making. In this paper, we aim to propose an objective method based on granular computing for determining the weights of the attribute sets. To address this issue, we first analyze the implied preorder relations under four evaluation forms and construct the corresponding preorder granular structures. Then, we define fuzzy measure of an attribute set by the similarity degree between a special preorder pairs. Finally, we employ two numerical examples for illustrating the feasibility and effectiveness of the proposed method. It is deserved to point out that the weight of each attribute subset can be learned from a given data set by the proposed method, not but be given subjectively by the decision maker. This idea provides a new perspective for multi-attribute decision making.

Multicriteria evaluation of animal welfare at farm level : an application of MCDA methodologies

Botreau R., Capdeville J., Perny P., Veissier I.

Foundations of Computing and Decision Sciences

2008

Vol. 33, No. 4

287-316

In this paper we present a contribution of Multicriteria Decision Analysis to the evaluation of Animal Welfare in European farms. We present the main features of the overall evaluation process designed to assess animal welfare on a farm from measures taken on the animals or their environment. We review the main steps of the construction of subcriteria and criteria. Then we discuss the aggregation problem and the design of a multicriteria sorting procedure to assess overall welfare from those criteria. This study is illustrated on cattle but is designed to be transposed to other animal species (e.g. pigs, poultry) so as to provide a general evaluation system for animal welfare on farms.