Choquet function

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Description

Calculates the value of a discrete Choquet integral of input x, with fuzzy measure in general representation

Usage

1
fm.Choquet(x, v, env=NULL)

Arguments

x

input vector of size n, containing utility value of input criteria. x is in [0,1].

v

the genral fuzzy measure of size m=2^n. Its values can be provided by users, or by estimating from empirical data.

env

Environment variable obtained from fm.Init(n).

Value

output

The ouput is a single value of the computed Choquet integral.

Author(s)

Gleb Beliakov, Andrei Kelarev, Quan Vu, Deakin University

References

[1] http://www.deakin.edu.au/~gleb/fmtools.html [2] H.Q. Vu, G. Beliakov, G. Li, 2014, A choquet integral toolbox and its application in customer preference analysis, in Data mining applications with R, Elsevier Inc., Waltham, MA., pp.247-272.

Examples

1
2
env<-fm.Init(3)
fm.Choquet(c(0.6, 0.3, 0.8), c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)

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