fm.ChoquetMob

This is an alternative calculation of the Choquet integral from the fuzzy measure in Mobius representation.

 Choquet 

Various tools for handling fuzzy measures, calculating Shapley value and interaction index, Choquet and Sugeno integrals, as well as fitting fuzzy measures to empirical data are provided. Construction of fuzzy measures from empirical data is done by solving a linear programming problem by using 'lpsolve' package, whose source in C adapted to the R environment
is included. The description of the basic theory of fuzzy measures is in the manual in the Doc folder in this package. Please refer to the following:
[1] <https://personal-sites.deakin.edu.au/~gleb/fmtools.html>
[2] G. Beliakov, H. Bustince, T. Calvo, 'A Practical Guide to Averaging', Springer, (2016, ISBN: 978-3-319-24753-3).
[3] G. Beliakov, S. James, J-Z. Wu, 'Discrete Fuzzy Measures', Springer, (2020, ISBN: 978-3-030-15305-2).

Gleb Beliakov

Rfmtool

Fuzzy Measure Tools

Quan Vu

Andrei Kelarev

Michel Berkelaar

Kjell Eikland

Samuel E. Buttrey

Stefan I. Larimore

Timothy A. Davis

John Gilbert

Esmond Ng

Peter Notebaert

Richard Stallman

Jeroen Dirks

Daniela L. Calderon

fm.ChoquetMob function

<dl> <dt>x</dt>
<dd>Input vector of size n, containing utility value of input criteria.
 x is in [0,1].
</dd> <dt>Mob</dt>
<dd>The Mobius fuzzy measure of size m=2^n. Its values can be provided by users,
 or by estimating from empirical data.
</dd> <dt>env</dt>
<dd>Environment variable obtained from fm.Init(n).</dd></dl>

Arguments

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

Author

Choquet integral value computation function in Mobius representation — fm.ChoquetMob

<dl>

 <dt>x</dt>
<dd>Input vector of size n, containing utility value of input criteria.
 x is in [0,1].
</dd>

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

 <dt>env</dt>
<dd>Environment variable obtained from fm.Init(n).</dd>

</dl>

Choquet integral value computation function in Mobius representation

fm.ChoquetMob: Choquet integral value computation function in Mobius representation

Description

Usage

Value

Arguments

Author

Examples