kappalab: Non-Additive Measure and Integral Manipulation Functions

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.

AuthorMichel Grabisch, Ivan Kojadinovic, Patrick Meyer.
Date of publication2015-07-18 17:00:04
MaintainerIvan Kojadinovic <ivan.kojadinovic@univ-pau.fr>
LicenseCeCILL
Version0.4-7

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

Functions

additive.capacity Man page
as.capacity Man page
as.capacity,card.capacity-method Man page
as.capacity,card.capacity-method Man page
as.capacity-methods Man page
as.capacity,set.func-method Man page
as.capacity,set.func-method Man page
as.card.capacity Man page
as.card.capacity,capacity-method Man page
as.card.capacity,capacity-method Man page
as.card.capacity,card.set.func-method Man page
as.card.capacity,card.set.func-method Man page
as.card.capacity-methods Man page
as.card.game Man page
as.card.game,card.set.func-method Man page
as.card.game,card.set.func-method Man page
as.card.game,game-method Man page
as.card.game,game-method Man page
as.card.game-methods Man page
as.card.set.func Man page
as.card.set.func-methods Man page
as.card.set.func,Mobius.card.set.func-method Man page
as.card.set.func,Mobius.set.func-method Man page
as.card.set.func,set.func-method Man page
as.card.set.func,set.func-method Man page
as.game Man page
as.game,card.game-method Man page
as.game,card.game-method Man page
as.game-methods Man page
as.game,set.func-method Man page
as.game,set.func-method Man page
as.Mobius.capacity Man page
as.Mobius.capacity-methods Man page
as.Mobius.capacity,Mobius.set.func-method Man page
as.Mobius.capacity,Mobius.set.func-method Man page
as.Mobius.card.set.func Man page
as.Mobius.card.set.func,card.set.func-method Man page
as.Mobius.card.set.func-methods Man page
as.Mobius.card.set.func,Mobius.set.func-method Man page
as.Mobius.card.set.func,Mobius.set.func-method Man page
as.Mobius.card.set.func,set.func-method Man page
as.Mobius.game Man page
as.Mobius.game-methods Man page
as.Mobius.game,Mobius.set.func-method Man page
as.Mobius.game,Mobius.set.func-method Man page
as.Mobius.set.func Man page
as.Mobius.set.func,card.set.func-method Man page
as.Mobius.set.func-methods Man page
as.Mobius.set.func,Mobius.card.set.func-method Man page
as.Mobius.set.func,Mobius.card.set.func-method Man page
as.Mobius.set.func,set.func-method Man page
as.set.func Man page
as.set.func,card.set.func-method Man page
as.set.func,card.set.func-method Man page
as.set.func-methods Man page
as.set.func,Mobius.card.set.func-method Man page
as.set.func,Mobius.set.func-method Man page
capacity Man page
capacity-class Man page
card.capacity Man page
card.capacity-class Man page
card.game Man page
card.game-class Man page
card.set.func Man page
card.set.func-class Man page
cdf.Choquet.unif Man page
cdf.Choquet.unif,game,numeric-method Man page
cdf.Choquet.unif-methods Man page
Choquet.integral Man page
Choquet.integral,card.game,numeric-method Man page
Choquet.integral,card.game,numeric-method Man page
Choquet.integral,game,numeric-method Man page
Choquet.integral,game,numeric-method Man page
Choquet.integral-methods Man page
Choquet.integral,Mobius.game,numeric-method Man page
Choquet.integral,Mobius.game,numeric-method Man page
conjugate Man page
conjugate,capacity-method Man page
conjugate,capacity-method Man page
conjugate,card.capacity-method Man page
conjugate,card.capacity-method Man page
conjugate,card.set.func-method Man page
conjugate,card.set.func-method Man page
conjugate-methods Man page
conjugate,set.func-method Man page
conjugate,set.func-method Man page
entropy Man page
entropy,capacity-method Man page
entropy,capacity-method Man page
entropy.capa.ident Man page
entropy,card.capacity-method Man page
entropy,card.capacity-method Man page
entropy-methods Man page
entropy,Mobius.capacity-method Man page
entropy,Mobius.capacity-method Man page
expect.Choquet.norm Man page
expect.Choquet.norm,game-method Man page
expect.Choquet.norm-methods Man page
expect.Choquet.norm,Mobius.game-method Man page
expect.Choquet.unif Man page
expect.Choquet.unif,game-method Man page
expect.Choquet.unif-methods Man page
favor Man page
favor,capacity-method Man page
favor,capacity-method Man page
favor,card.capacity-method Man page
favor,card.capacity-method Man page
favor-methods Man page
favor,Mobius.capacity-method Man page
favor,Mobius.capacity-method Man page
game Man page
game-class Man page
heuristic.ls.capa.ident Man page
interaction.indices Man page
interaction.indices,card.set.func-method Man page
interaction.indices,card.set.func-method Man page
interaction.indices-methods Man page
interaction.indices,Mobius.set.func-method Man page
interaction.indices,Mobius.set.func-method Man page
interaction.indices,set.func-method Man page
interaction.indices,set.func-method Man page
is.cardinal Man page
is.cardinal,card.set.func-method Man page
is.cardinal,card.set.func-method Man page
is.cardinal-methods Man page
is.cardinal,Mobius.set.func-method Man page
is.cardinal,Mobius.set.func-method Man page
is.cardinal,set.func-method Man page
is.cardinal,set.func-method Man page
is.kadditive Man page
is.kadditive,card.set.func,numeric-method Man page
is.kadditive,card.set.func,numeric-method Man page
is.kadditive-methods Man page
is.kadditive,Mobius.set.func,numeric-method Man page
is.kadditive,Mobius.set.func,numeric-method Man page
is.kadditive,set.func,numeric-method Man page
is.kadditive,set.func,numeric-method Man page
is.monotone Man page
is.monotone,card.set.func-method Man page
is.monotone,card.set.func-method Man page
is.monotone-methods Man page
is.monotone,Mobius.set.func-method Man page
is.monotone,Mobius.set.func-method Man page
is.monotone,set.func-method Man page
is.monotone,set.func-method Man page
is.normalized Man page
is.normalized,capacity-method Man page
is.normalized,capacity-method Man page
is.normalized,card.capacity-method Man page
is.normalized,card.capacity-method Man page
is.normalized-methods Man page
is.normalized,Mobius.capacity-method Man page
is.normalized,Mobius.capacity-method Man page
k.truncate.Mobius Man page
k.truncate.Mobius-methods Man page
k.truncate.Mobius,Mobius.set.func,numeric-method Man page
k.truncate.Mobius,Mobius.set.func,numeric-method Man page
k.truncate.Mobius,set.func,numeric-method Man page
k.truncate.Mobius,set.func,numeric-method Man page
least.squares.capa.ident Man page
lin.prog.capa.ident Man page
lower.capacity Man page
ls.ranking.capa.ident Man page
ls.sorting.capa.ident Man page
ls.sorting.treatment Man page
mini.dist.capa.ident Man page
mini.var.capa.ident Man page
Mobius Man page
Mobius.capacity Man page
Mobius.capacity-class Man page
Mobius,capacity-method Man page
Mobius,capacity-method Man page
Mobius.card.set.func Man page
Mobius.card.set.func-class Man page
Mobius,card.set.func-method Man page
Mobius,card.set.func-method Man page
Mobius.game Man page
Mobius.game-class Man page
Mobius,game-method Man page
Mobius,game-method Man page
Mobius-methods Man page
Mobius.set.func Man page
Mobius.set.func-class Man page
Mobius,set.func-method Man page
Mobius,set.func-method Man page
normalize Man page
normalize,capacity-method Man page
normalize,card.capacity-method Man page
normalize-methods Man page
normalize,Mobius.capacity-method Man page
orness Man page
orness,capacity-method Man page
orness,capacity-method Man page
orness,card.capacity-method Man page
orness,card.capacity-method Man page
orness-methods Man page
orness,Mobius.capacity-method Man page
orness,Mobius.capacity-method Man page
pdf.Choquet.unif Man page
pdf.Choquet.unif,game,numeric-method Man page
pdf.Choquet.unif-methods Man page
rnd Man page
rnd-methods Man page
rnd,superclass.set.func-method Man page
sd.Choquet.norm Man page
sd.Choquet.norm,game-method Man page
sd.Choquet.norm-methods Man page
sd.Choquet.unif Man page
sd.Choquet.unif,game-method Man page
sd.Choquet.unif-methods Man page
set.func Man page
set.func-class Man page
Shapley.value Man page
Shapley.value,card.set.func-method Man page
Shapley.value,card.set.func-method Man page
Shapley.value-methods Man page
Shapley.value,Mobius.set.func-method Man page
Shapley.value,Mobius.set.func-method Man page
Shapley.value,set.func-method Man page
Shapley.value,set.func-method Man page
show,ANY-method Man page
show,classRepresentation-method Man page
show,genericFunction-method Man page
show,MethodDefinition-method Man page
show-methods Man page
show,MethodWithNext-method Man page
show,Mobius.set.func-method Man page
show,ObjectsWithPackage-method Man page
show,set.func-method Man page
show,summary.superclass.capacity-method Man page
show,summary.superclass.capacity-method Man page
show,summary.superclass.set.func-method Man page
show,summary.superclass.set.func-method Man page
show,superclass.set.func-method Man page
show,superclass.set.func-method Man page
show,traceable-method Man page
Sipos.integral Man page
Sipos.integral,card.game,numeric-method Man page
Sipos.integral,card.game,numeric-method Man page
Sipos.integral,game,numeric-method Man page
Sipos.integral,game,numeric-method Man page
Sipos.integral-methods Man page
Sipos.integral,Mobius.game,numeric-method Man page
Sipos.integral,Mobius.game,numeric-method Man page
Sugeno.integral Man page
Sugeno.integral,card.game,numeric-method Man page
Sugeno.integral,card.game,numeric-method Man page
Sugeno.integral,game,numeric-method Man page
Sugeno.integral,game,numeric-method Man page
Sugeno.integral-methods Man page
Sugeno.integral,Mobius.game,numeric-method Man page
Sugeno.integral,Mobius.game,numeric-method Man page
summary Man page
summary,ANY-method Man page
summary-methods Man page
summary.superclass.capacity-class Man page
summary,superclass.capacity-method Man page
summary,superclass.capacity-method Man page
summary.superclass.set.func-class Man page
summary,superclass.set.func-method Man page
summary,superclass.set.func-method Man page
superclass.capacity-class Man page
superclass.set.func-class Man page
to.data.frame Man page
to.data.frame,card.set.func-method Man page
to.data.frame,card.set.func-method Man page
to.data.frame-methods Man page
to.data.frame,Mobius.card.set.func-method Man page
to.data.frame,Mobius.card.set.func-method Man page
to.data.frame,Mobius.set.func-method Man page
to.data.frame,Mobius.set.func-method Man page
to.data.frame,set.func-method Man page
to.data.frame,set.func-method Man page
uniform.capacity Man page
upper.capacity Man page
variance Man page
variance,capacity-method Man page
variance,capacity-method Man page
variance,card.capacity-method Man page
variance,card.capacity-method Man page
variance-methods Man page
variance,Mobius.capacity-method Man page
variance,Mobius.capacity-method Man page
veto Man page
veto,capacity-method Man page
veto,capacity-method Man page
veto,card.capacity-method Man page
veto,card.capacity-method Man page
veto-methods Man page
veto,Mobius.capacity-method Man page
veto,Mobius.capacity-method Man page
zeta Man page
zeta-methods Man page
zeta,Mobius.capacity-method Man page
zeta,Mobius.capacity-method Man page
zeta,Mobius.card.set.func-method Man page
zeta,Mobius.card.set.func-method Man page
zeta,Mobius.game-method Man page
zeta,Mobius.game-method Man page
zeta,Mobius.set.func-method Man page
zeta,Mobius.set.func-method Man page

Files

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

Questions? Problems? Suggestions? or email at ian@mutexlabs.com.

Please suggest features or report bugs with the GitHub issue tracker.

All documentation is copyright its authors; we didn't write any of that.