Methods for computing the probability density and cumulative distribution functions of the Choquet integral with respect to a game for evaluations uniformly distributed on the unit hypercube.
This function estimates a capacity using as argument a set of data under the form: datum=(score on attribute 1, ..., score on attribute n). The approach roughly consists in replacing the subjective notion of importance of a subset of attributes by that of information content of a subset of attributes, which is estimated from the data by means of a parametric entropy measure. For more details, see the references hereafter.
● Data Source:
CranContrib
● Keywords: math
● Alias: entropy.capa.ident
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Computes the Shapley value (n indices) of a set function. The set function can be given either under the form of an object of class set.func, card.set.func or Mobius.set.func.
Computes the Sugeno integral of a non negative function with respect to a game. Moreover, if the game is a capacity, the range of the function must be contained into the range of the capacity. The game can be given either under the form of an object of class game, card.game or Mobius.game.
ls.ranking.capa.ident
(Package: kappalab) :
Least squares capacity identification in the framework of a ranking procedure
Ranking alternatives means ordering them from the best to the worst alternative. The aim of the implemented method is to model a given ranking by means of a Choquet integral. The result of the function is an object of class Mobius.capacity. This function is an implementation of the TOMASO method (see Meyer and Roubens (2005)) in the particular ranking framework. The input data are given under the form of a set of alternatives and a partial weak order, each alternative being described according to a set of criteria. These well-known alternatives are called "prototypes". They represent alternatives for which the decision maker has an a priori knowledge and for which he/she is able to build a ranking. If the provided ranking (partial weak order) of the prototypes cannot be described by a Choquet integral, an approximative solution, which minimizes the "gap" between the given ranking and the one derived from the Choquet integral, is proposed. The problem is solved by quadratic programming.
● Data Source:
CranContrib
● Keywords: math
● Alias: ls.ranking.capa.ident
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0 images
set.func
(Package: kappalab) :
Create objects of class "set.func", "game", or "capacity".
These functions create objects of class set.func, game, or capacity from objects of class numeric.
● Data Source:
CranContrib
● Keywords: math
● Alias: capacity, game, set.func
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0 images
Computes the Choquet integral of a discrete function with respect to a game. The game can be given either under the form of an object of class game, card.game or Mobius.game. If the integrand is not positive, this function computes what is known as the asymmetric Choquet integral.
providing 
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