kappalab: Non-Additive Measure and Integral Manipulation Functions

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S4 tool box for capacity (or non-additive measure, fuzzy measure) and integral manipulation in a finite setting. It contains routines for handling various types of set functions such as games or capacities. It can be used to compute several non-additive integrals: the Choquet integral, the Sugeno integral, and the symmetric and asymmetric Choquet integrals. An analysis of capacities in terms of decision behavior can be performed through the computation of various indices such as the Shapley value, the interaction index, the orness degree, etc. The well-known Mbius transform, as well as other equivalent representations of set functions can also be computed. Kappalab further contains seven capacity identification routines: three least squares based approaches, a method based on linear programming, a maximum entropy like method based on variance minimization, a minimum distance approach and an unsupervised approach based on parametric entropies. The functions contained in Kappalab can for instance be used in the framework of multicriteria decision making or cooperative game theory.

Author
Michel Grabisch, Ivan Kojadinovic, Patrick Meyer.
Date of publication
2015-07-18 17:00:04
Maintainer
Ivan Kojadinovic <ivan.kojadinovic@univ-pau.fr>
License
CeCILL
Version
0.4-7

View on CRAN

Man pages

as.capacity-methods
Coercion method
as.card.capacity-methods
Coercion method
as.card.game-methods
Coercion method
as.card.set.func-methods
Coercion method
as.game-methods
Coercion method
as.Mobius.capacity-methods
Coercion method
as.Mobius.card.set.func-methods
Coercion method
as.Mobius.game-methods
Coercion method
as.Mobius.set.func-methods
Coercion method
as.set.func-methods
Coercion method
capacity-class
Class "capacity"
card.capacity-class
Class "card.capacity"
card.game-class
Class "card.game"
card.set.func-class
Class "card.set.func"
card.set.func.gen
Create objects representing cardinal set functions.
Choquet.integral-methods
Choquet integral
conjugate-methods
The conjugate (or dual) transform
entropy.capa.ident
Unsupervised identification of a capacity from profiles
entropy-methods
Normalized entropy of a capacity
expect.Choquet.unif-methods
Expectation and standard deviation of the Choquet integral in...
favor-methods
Favor indices
game-class
Class "game"
heuristic.ls.capa.ident
Heuristic least squares capacity identification
interaction.indices-methods
The Shapley interaction indices
is.cardinal-methods
Test method
is.kadditive-methods
Test method
is.monotone-methods
Test method
is.normalized-methods
Test method
k.truncate.Mobius-methods
k-order truncation of the M<f6>bius representation of a set...
least.squares.capa.ident
Least squares capacity identification
lin.prog.capa.ident
Capacity identification based on linear programming
ls.ranking.capa.ident
Least squares capacity identification in the framework of a...
ls.sorting.capa.ident
Least squares capacity identification in the framework of a...
ls.sorting.treatment
Least squares capacity identification in the framework of a...
mini.dist.capa.ident
Minimum distance capacity identification
mini.var.capa.ident
Minimum variance capacity identification
Mobius.capacity-class
Class "Mobius.capacity"
Mobius.card.gen
Creates an object representing the M<f6>bius transform of a...
Mobius.card.set.func-class
Class "Mobius.card.set.func"
Mobius.game-class
Class "Mobius.game"
Mobius.gen
Create objects representing the M<f6>bius transform of a set...
Mobius-methods
The M<f6>bius transform
Mobius.set.func-class
Class "Mobius.set.func"
normalize-methods
Normalizes a capacity.
orness-methods
Orness degree
pdf.Choquet.unif-methods
Distribution of the Choquet integral for evaluations...
rnd-methods
Rounding of set function coefficients
set.func-class
Class "set.func"
set.func.gen
Create objects of class "set.func", "game", or "capacity".
Shapley.value-methods
The Shapley value
show-methods
Methods for Function show in Package 'kappalab'
Sipos.integral-methods
Sipos integral
Sugeno.integral-methods
Sugeno integral
summary-methods
Summary method
summary.superclass.capacity-class
Class "summary.superclass.capacity"
summary.superclass.set.func-class
Class "summary.superclass.set.func"
superclass.capacity-class
Class "superclass.capacity"
superclass.set.func-class
Class "superclass.set.func"
to.data.frame-methods
Puts a set function under the form of a data.frame
variance-methods
Normalized variance of a capacity
veto-methods
Veto indices
zeta-methods
The zeta transform

Files in this package

kappalab
kappalab/COPYING
kappalab/tests
kappalab/tests/set.func-class.R
kappalab/tests/card.capacity-class.R
kappalab/tests/entropy-methods.R
kappalab/tests/is.monotone-methods.R
kappalab/tests/least.squares.capa.ident.R
kappalab/tests/Choquet.integral-methods.R
kappalab/tests/is.kadditive-methods.R
kappalab/tests/capacity-class.R
kappalab/tests/orness-methods.R
kappalab/tests/card.set.func-class.R
kappalab/tests/veto-methods.R
kappalab/tests/mini.dist.capa.ident.R
kappalab/tests/is.cardinal-methods.R
kappalab/tests/variance-methods.R
kappalab/tests/Mobius.capacity-class.R
kappalab/tests/interaction.indices-methods.R
kappalab/tests/card.game-class.R
kappalab/tests/Mobius.set.func-class.R
kappalab/tests/heuristic.ls.capa.ident.R
kappalab/tests/conjugate-methods.R
kappalab/tests/ls.sorting.treatment.R
kappalab/tests/k.truncate.Mobius-methods.R
kappalab/tests/entropy.capa.ident.R
kappalab/tests/Mobius.card.set.func-class.R
kappalab/tests/lin.prog.capa.ident.R
kappalab/tests/Shapley.value-methods.R
kappalab/tests/mini.var.capa.ident.R
kappalab/tests/to.data.frame-methods.R
kappalab/tests/Mobius-methods.R
kappalab/tests/Mobius.game-class.R
kappalab/src
kappalab/src/core.h
kappalab/src/Mobius.bounds.h
kappalab/src/least.squares.c
kappalab/src/constraints.c
kappalab/src/constraints.h
kappalab/src/core.c
kappalab/src/min.dist.c
kappalab/src/least.squares.h
kappalab/src/cdf.Choquet.h
kappalab/src/moments.Choquet.h
kappalab/src/heuristic.ls.c
kappalab/src/cdf.Choquet.c
kappalab/src/min.dist.h
kappalab/src/min.var.h
kappalab/src/min.var.c
kappalab/src/moments.Choquet.c
kappalab/src/Mobius.bounds.c
kappalab/NAMESPACE
kappalab/R
kappalab/R/card.set.func.R
kappalab/R/Mobius.set.func.R
kappalab/R/internals.R
kappalab/R/AllClass.R
kappalab/R/card.game.R
kappalab/R/least.squares.capa.ident.R
kappalab/R/set.func.R
kappalab/R/Mobius.card.set.func.R
kappalab/R/ls.sorting.capa.ident.R
kappalab/R/superclass.capacity.R
kappalab/R/mini.dist.capa.ident.R
kappalab/R/Mobius.capacity.R
kappalab/R/game.R
kappalab/R/Mobius.game.R
kappalab/R/heuristic.ls.capa.ident.R
kappalab/R/superclass.set.func.R
kappalab/R/AllGeneric.R
kappalab/R/ls.sorting.treatment.R
kappalab/R/capacity.R
kappalab/R/card.capacity.R
kappalab/R/constraints.R
kappalab/R/entropy.capa.ident.R
kappalab/R/lin.prog.capa.ident.R
kappalab/R/mini.var.capa.ident.R
kappalab/R/ls.ranking.capa.ident.R
kappalab/MD5
kappalab/DESCRIPTION
kappalab/man
kappalab/man/summary-methods.Rd
kappalab/man/pdf.Choquet.unif-methods.Rd
kappalab/man/Mobius.card.set.func-class.Rd
kappalab/man/entropy.capa.ident.Rd
kappalab/man/Shapley.value-methods.Rd
kappalab/man/Sugeno.integral-methods.Rd
kappalab/man/ls.ranking.capa.ident.Rd
kappalab/man/set.func.gen.Rd
kappalab/man/Choquet.integral-methods.Rd
kappalab/man/Mobius-methods.Rd
kappalab/man/is.kadditive-methods.Rd
kappalab/man/ls.sorting.treatment.Rd
kappalab/man/rnd-methods.Rd
kappalab/man/as.card.set.func-methods.Rd
kappalab/man/conjugate-methods.Rd
kappalab/man/as.set.func-methods.Rd
kappalab/man/is.monotone-methods.Rd
kappalab/man/heuristic.ls.capa.ident.Rd
kappalab/man/card.set.func.gen.Rd
kappalab/man/capacity-class.Rd
kappalab/man/as.game-methods.Rd
kappalab/man/as.Mobius.set.func-methods.Rd
kappalab/man/Mobius.card.gen.Rd
kappalab/man/as.card.capacity-methods.Rd
kappalab/man/Sipos.integral-methods.Rd
kappalab/man/interaction.indices-methods.Rd
kappalab/man/favor-methods.Rd
kappalab/man/game-class.Rd
kappalab/man/as.capacity-methods.Rd
kappalab/man/card.game-class.Rd
kappalab/man/variance-methods.Rd
kappalab/man/Mobius.game-class.Rd
kappalab/man/mini.var.capa.ident.Rd
kappalab/man/as.card.game-methods.Rd
kappalab/man/Mobius.capacity-class.Rd
kappalab/man/Mobius.gen.Rd
kappalab/man/least.squares.capa.ident.Rd
kappalab/man/summary.superclass.capacity-class.Rd
kappalab/man/veto-methods.Rd
kappalab/man/card.capacity-class.Rd
kappalab/man/set.func-class.Rd
kappalab/man/normalize-methods.Rd
kappalab/man/superclass.capacity-class.Rd
kappalab/man/superclass.set.func-class.Rd
kappalab/man/is.cardinal-methods.Rd
kappalab/man/entropy-methods.Rd
kappalab/man/as.Mobius.game-methods.Rd
kappalab/man/as.Mobius.card.set.func-methods.Rd
kappalab/man/is.normalized-methods.Rd
kappalab/man/zeta-methods.Rd
kappalab/man/card.set.func-class.Rd
kappalab/man/summary.superclass.set.func-class.Rd
kappalab/man/lin.prog.capa.ident.Rd
kappalab/man/to.data.frame-methods.Rd
kappalab/man/ls.sorting.capa.ident.Rd
kappalab/man/orness-methods.Rd
kappalab/man/as.Mobius.capacity-methods.Rd
kappalab/man/mini.dist.capa.ident.Rd
kappalab/man/k.truncate.Mobius-methods.Rd
kappalab/man/expect.Choquet.unif-methods.Rd
kappalab/man/Mobius.set.func-class.Rd
kappalab/man/show-methods.Rd