24,693 research outputs found
Axiomatizations of quasi-polynomial functions on bounded chains
Two emergent properties in aggregation theory are investigated, namely
horizontal maxitivity and comonotonic maxitivity (as well as their dual
counterparts) which are commonly defined by means of certain functional
equations. We completely describe the function classes axiomatized by each of
these properties, up to weak versions of monotonicity in the cases of
horizontal maxitivity and minitivity. While studying the classes axiomatized by
combinations of these properties, we introduce the concept of quasi-polynomial
function which appears as a natural extension of the well-established notion of
polynomial function. We give further axiomatizations for this class both in
terms of functional equations and natural relaxations of homogeneity and median
decomposability. As noteworthy particular cases, we investigate those
subclasses of quasi-term functions and quasi-weighted maximum and minimum
functions, and provide characterizations accordingly
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
An empirical study of statistical properties of Choquet and Sugeno integrals
This paper investigates the statistical properties of the Choquet and Sugeno integrals, used as multiattribute models. The investigation is done on an empirical basis, and focuses on two topics: the distribution of the output of these integrals when the input is corrupted with noise, and the robustness of these models, when they are identified using some set of learning data through some learning procedure.Choquet integral; Sugeno integral; output distribution
Invariant functionals on completely distributive lattices
In this paper we are interested in functionals defined on completely
distributive lattices and which are invariant under mappings preserving
{arbitrary} joins and meets. We prove that the class of nondecreasing invariant
functionals coincides with the class of Sugeno integrals associated with
-valued capacities, the so-called term functionals, thus extending
previous results both to the infinitary case as well as to the realm of
completely distributive lattices. Furthermore, we show that, in the case of
functionals over complete chains, the nondecreasing condition is redundant.
Characterizations of the class of Sugeno integrals, as well as its superclass
comprising all polynomial functionals, are provided by showing that the
axiomatizations (given in terms of homogeneity) of their restriction to
finitary functionals still hold over completely distributive lattices. We also
present canonical normal form representations of polynomial functionals on
completely distributive lattices, which appear as the natural extensions to
their finitary counterparts, and as a by-product we obtain an axiomatization of
complete distributivity in the case of bounded lattices
Organic Farming in Europe by 2010: Scenarios for the future
How will organic farming in Europe evolve by the year 2010? The answer provides a basis for the development of different policy options and for anticipating the future relative competitiveness of organic and conventional farming. The authors tackle the question using an innovative approach based on scenario analysis, offering the reader a range of scenarios that encompass the main possible evolutions of the organic farming sector.
This book constitutes an innovative and reliable decision-supporting tool for policy makers, farmers and the private sector. Researchers and students operating in the field of agricultural economics will also benefit from the methodological approach adopted for the scenario analysis
Inconsistency and non-additive Choquet integration in the Analytic Hierarchy Process
We propose to extend the aggregation scheme of Saaty’s AHP, from the stan- dard weighted averaging to the more general Choquet integration. In our model, a measure of inconsistency between criteria is derived from the main pairwise comparison matrix and it is used to construct a non-additive capacity, whose associated Choquet integral reduces to the standard weighted mean in the con- sistency case. In the general inconsistency case, however, the new aggregation scheme based on Choquet integration tends to attenuate (resp. emphasize) the priority values of the criteria with higher (resp. lower) average inconsistency with the remaining criteria.Aggregation Functions, Multiple Criteria Analysis, AHP, Inconsintency, non-additive measures, Choquet integral, and Shapley values.
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