fm.ChoquetCoMobKInter {Rfmtool}

function for calculating Choquet integral value with respect to dual k-interactive fuzzy measure in Mobius representation

Description

Calculates the Choquet integral of x with respect to dual k-interactive fuzzy measure in Mobius representation.

Usage

fm.ChoquetCoMobKInter(x, Mob, kadd, env=NULL)

Arguments

x

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

Mob

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

kadd

is the value of k-additivity, which is used for reducing the complexity of fuzzy measures. kadd is defined as an optional argument, its default value is kadd = n. kadd is k in k-additive f-measure, 1 < kadd < n+1; if kdd=n - f.m. is unrestricted.

env

Environment variable obtained from fm.Init(n).

Value

output

The output is the Choquet integral value in Mobius representation.

Author(s)

Gleb Beliakov, Andrei Kelarev, Quan Vu, Daniela L. Calderon, Deakin University

Examples

env <-fm.Init(4)
step <- 0.0001
Fn <- NULL
fuzzymeasures <- fm.generate_fm_kinteractivedualconvex(1, 4, 2, 1000, step, Fn, env)
fuzzymeasures
env

fm.ChoquetCoMobKInter(c(0.2,0.5,0.4,0.1), fuzzymeasures$V, 2, env)
env<-fm.Free(env)