Rfmtool (version 5.0.3)

fm.ChoquetCoMobKInter: 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)

Value

output

The output is the Choquet integral value in Mobius representation.

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).

Author

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)