64 research outputs found
Fuzzy measures and integrals in MCDA
This chapter aims at a unified presentation of various methods of MCDA based onfuzzy measures (capacity) and fuzzy integrals, essentially the Choquet andSugeno integral. A first section sets the position of the problem ofmulticriteria decision making, and describes the various possible scales ofmeasurement (difference, ratio, and ordinal). Then a whole section is devotedto each case in detail: after introducing necessary concepts, the methodologyis described, and the problem of the practical identification of fuzzy measuresis given. The important concept of interaction between criteria, central inthis chapter, is explained in details. It is shown how it leads to k-additivefuzzy measures. The case of bipolar scales leads to thegeneral model based on bi-capacities, encompassing usual models based oncapacities. A general definition of interaction for bipolar scales isintroduced. The case of ordinal scales leads to the use of Sugeno integral, andits symmetrized version when one considers symmetric ordinal scales. Apractical methodology for the identification of fuzzy measures in this contextis given. Lastly, we give a short description of some practical applications.Choquet integral; fuzzy measure; interaction; bi-capacities
A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid
The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a better interpretation of the models and a better use of the Choquet integral in multi-criteria decision aid. Parallel to these theoretical works, the Choquet integral has been applied to many new fields, and several softwares and libraries dedicated to this model have been developed.Choquet integral, Sugeno integral, capacity, bipolarity, preferences
Representation of preferences over a finite scale by a mean operator
Suppose that a decision maker provides a weak order on a given set of alternatives, each alternative being described by a vector of scores, which are given on a finite ordinal scale . The paper addresses the question of the representation of this weak order by some mean operator, and gives necessary and sufficient conditions for such a representation, with possible shrinking and/or refinement of the scale .preference representation, finite scale, meanoperator, aggregation of scores, refinement of scale
Characterizations of discrete Sugeno integrals as polynomial functions over distributive lattices
We give several characterizations of discrete Sugeno integrals over bounded
distributive lattices, as particular cases of lattice polynomial functions,
that is, functions which can be represented in the language of bounded lattices
using variables and constants. We also consider the subclass of term functions
as well as the classes of symmetric polynomial functions and weighted minimum
and maximum functions, and present their characterizations, accordingly.
Moreover, we discuss normal form representations of these functions
Bipolar Fuzzy Integrals
In decision analysis and especially in multiple criteria decision analysis,
several non additive integrals have been introduced in the last sixty years.
Among them, we remember the Choquet integral, the Shilkret integral and the
Sugeno integral. Recently, the bipolar Choquet integral has been proposed for
the case in which the underlying scale is bipolar. In this paper we propose the
bipolar Shilkret integral and the bipolar Sugeno integral. Moreover, we provide
an axiomatic characterization of all these three bipolar fuzzy integrals.Comment: 15 page
Modeling attitudes toward uncertainty through the use of the Sugeno integral
The aim of the paper is to present under uncertainty, and in an ordinal framework, an axiomatic treatment of the Sugeno integral in terms of preferences which parallels some earlier derivations devoted to the Choquet integral. Some emphasis is given to the characterization of uncertainty aversion.Sugeno integral; uncertainty aversion; preference relations; ordinal information
Robust Integrals
In decision analysis and especially in multiple criteria decision analysis,
several non additive integrals have been introduced in the last years. Among
them, we remember the Choquet integral, the Shilkret integral and the Sugeno
integral. In the context of multiple criteria decision analysis, these
integrals are used to aggregate the evaluations of possible choice
alternatives, with respect to several criteria, into a single overall
evaluation. These integrals request the starting evaluations to be expressed in
terms of exact-evaluations. In this paper we present the robust Choquet,
Shilkret and Sugeno integrals, computed with respect to an interval capacity.
These are quite natural generalizations of the Choquet, Shilkret and Sugeno
integrals, useful to aggregate interval-evaluations of choice alternatives into
a single overall evaluation. We show that, when the interval-evaluations
collapse into exact-evaluations, our definitions of robust integrals collapse
into the previous definitions. We also provide an axiomatic characterization of
the robust Choquet integral.Comment: 24 page
Modeling attitudes toward uncertainty through the use of the Sugeno integral
International audienceThe aim of the paper is to present under uncertainty, and in an ordinal framework, an axiomatic treatment of the Sugeno integral in terms of preferences which parallels some earlier derivations devoted to the Choquet integral. Some emphasis is given to the characterization of uncertainty aversion
Explicit Descriptions of Bisymmetric Sugeno Integrals
We provide sufficient conditions for a Sugeno integral to be bisymmetric. We explicitly describe bisymmetric Sugeno integrals over chains
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