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Rfmtool (version 5.0.3)

Fuzzy Measure Tools

Description

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] [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).

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Version

Install

install.packages('Rfmtool')

Monthly Downloads

617

Version

5.0.3

License

LGPL-3

Maintainer

Gleb Beliakov

Last Published

May 30th, 2024

Functions in Rfmtool (5.0.3)

Choquet integral value computation function in Mobius representation

Interaction Index computation function

fm.IsMeasureKmaxitive

IsMeasureKmaxitive function

fm.IsMeasureSupermodular

IsMeasureSupermodular function

fm.IsMeasureKmaxitiveMob

IsMeasureKmaxitive function in Mobius representation

fm.IsMeasureSuperadditive

IsMeasureSuperadditive function

fm.IsMeasureBalanced

IsMeasureBalanced function

fm.IsMeasureSuperadditiveMob

IsMeasureSuperadditive function in Mobius representation

fm.IsMeasureSupermodularMob

IsMeasureSupermodular function in Mobius representation

fm.ChoquetMob_sparse

Choquet integral computation function in sparse representation

fm.IsMeasureBalancedMob

IsMeasureBalanced function in Mobius representation

fm.NonmodularityIndexMobkadditive

Function for calculating all Nonmodularity indices of k-additive in Mobius representation

Mobius transform function

fm.InteractionBMob

Banzhaf InteractionB Index computation function in Mobius representation

fm.IsMeasureSubmodularMob

IsMeasureSubmodular function in Mobius representation

fm.NonmodularityIndexKinteractive

NonmodularityIndexKinteractive computation function

fm.NonadditivityIndexMob

Nonadditivity index computation function in Mobius representation

fm.IsMeasureSubadditiveMob

IsMeasureSub additive function in Mobius representation

fm.IsMeasureSubadditive

IsMeasureSub additive function

fm.IsMeasureAdditiveMob

IsMeasureAdditive function in Mobius representation

fm.IsMeasureAdditive

IsMeasureAdditive function

fm.InteractionMob

Interaction Index computation function for Mobius fuzzy measure

fm.InteractionB

Banzhaf Interaction Index computation function

fm.NonmodularityIndex_sparse

Nonmodularity index computation function in sparse representation

Shapley value computation function in Mobius representation

fm.IsMeasureSubmodular

IsMeasureSub modular function

fm.IsMeasureSelfdual

IsMeasureSelfdual function

fm.IsMeasureSelfdualMob

IsMeasureSelfdual function in Mobius representation

fm.NonmodularityIndex

Nonmodularity index computation function

fm.ShowCoalitions

Show Coalitions function

fm.IsMeasureSymmetricMob

IsMeasureSymmetric function in Mobius representation

fm.IsMeasureSymmetric

IsMeasureSymmetric function

fm.NonmodularityIndexMob

Nonmodularityindex computation function in Mobius representation

fm.ShapleyMob_sparse

Shapley values computation function in sparse representation

fm.NonadditivityIndex

Nonadditivity index computation function

fm.PrepareSparseFM

PrepareSparseFM preparation function

fm.OrnessChoquet

OrnessChoquet function

Rfmtool package

fm.expand_2add_full

Function for exporting full representation of 2-additive capacity

fm.ShowCoalitionsCard

Show CoalitionsCard function

Shapley value computation function

fm.check_convexity_monotonicity_mob

Function for checking supermodularity of the set function v in Mobius representation

fm.OrnessChoquetMob

OrnessChoquet function in Mobius representation

Sugeno computation function

fm.check_monotonicity

Function for checking monotonicity of the set function v

fm.Shapley2addMob

Function for calculating Shapley values of 2-additive fuzzy measure in Mobius representation

Zeta transform function

fm.add_singletons_sparse

Function for adding singletons to the sparse fuzzy measure

fm.fitting2additive

Fuzzy Measure Fitting function

fm.expand_sparse_full

Function for exporting full capacity from sparse representation

fm.fittingKinteractive

Fuzzy Measure Fitting function

fm.add_pair_sparse

Function for adding a pair to the sparse fuzzy measure

fm.add_tuple_sparse

Function for adding singletons to the sparse fuzzy measure

Sugeno function in Mobius representation

Mobius Fuzzy Measure Fitting function

Function for calculating dual of k-additive fuzzy measure in Mobius representation

fm.export_maximal_chains

Function for exporting maximal chains

Basic error check

Function for calculating dual of fuzzy measure

fm.check_monotonicity_mob

Function for checking monotonicity of the set function v in Mobius representation.

fm.fittingKinteractiveAuto

Fuzzy Measure Fitting function of the k-interactive

Dualm computation function in Mobius representation

FreeSparseFM function

Symmetric Fuzzy Measure Fitting function

fm.check_monotonicity_mob_2additive

Function for checking the monotonicity of the 2-additive set function v in Mobius representation.

fm.fittingKinteractiveMC

Fuzzy Measure Fitting function of the k-interactive using maximal chains method

fm.FreeSparseFM

FreeSparseFM function

fm.generate_fm_tsort

Function for random generation of fuzzy measures

fm.generate_fm_sorting

Function for random generation of fuzzy measures in standard representation

fm.check_monotonicity_sort_insert

Function for checking monotonicity of the set function v

fm.check_monotonicity_sort_merge

Function for checking monotonicity of the set function v

Fuzzy Measure Fitting function

fm.generate_fm_2additive_convex_sparse

Function for generating 2additive convex numbers in sparse representation

fm.generate_fm_2additive_convex_withsomeindependent

Function for generating 2additive convex fuzzy measures with some independent inputs

fm.get_sizearray_tuples

Function for exporting the size of the array of tuples

fm.generate_fm_2additive_concave

Function for generating 2additive concave fuzzy measures.

fm.generate_fm_2additive_convex

Function for generating 2-additive convex fuzzy measures

fm.is_inset_sparse

Function for checking if i belongs to the tuple A

fm.generate_belief

Function for random generation of belief fuzzy measures in standard representation

fm.fittingKmaxitive

Fuzzy Measure Fitting function of the k-maxitive

fm.sparse_get_singletons

Get singletons of sparse fuzzy measure

fm.fittingKtolerant

Fuzzy Measure Fitting function of the k-tolerant

Additive Fuzzy Measure Fitting function

fm.generate_fm_minplus

Generate randomly fuzzy measures

fm.fm_arraysize

Function for returning the length of the array

fm.generate_fm_2additive

Function for generating 2-additive fuzzy measures in Mobius representation

fm.populate_fm_2add_sparse_from2add

Function for populating 2-additive sparse capacity from 2-additive capacity

fm.generate_fm_randomwalk

Function for generating several k-additive fuzzy measure

fm.sparse_get_pairs

Get pairs computation function in sparse representation

fm.fittingKinteractiveMarginal

Fuzzy Measure Fitting function of the k-interactive using marginal representation

fm.generate_antibuoyant

Function for generating one antibuoyant random fuzzy measure

fm.fittingKinteractiveMarginalMC

Fuzzy Measure Fitting function of the k-interactive using marginal representation and maximal chains method

fm.generate_balanced

Function for random generation of balanced fuzzy measures in standard representation

fm.generate_fm_2additive_randomwalk2

Function for generating random 2-additive fuzzy measures in Mobius representation by using random walk.

fm.sparse_get_tuples

Get tuples of a sparse fuzzy measure

fm.generate_fm_kadditive_convex_sparse

Generate kadditive convex sparse fuzzy measures

fm.min_subset_sparse

Minimun of x computation function in sparse representation

fm.generate_fm_kinteractivedualconcave

Function for generating k-interactive dual concave fuzzy measures in Mobius representation

fm.generate_fm_kinteractivedualconvex

Function for generating several k-interactive dual convex fuzzy measures in Mobius representation

fm.populate_fm_2add_sparse

Function for populating 2-additive sparse capacity

fm.tuple_cardinality_sparse

Tuple cardinality

fm.is_subset_sparse

Function for checking if tuple B is subset of tuple A

fm.max_subset_sparse

Maximun of x computation function in sparse representation

fm.generate_fmconvex_tsort

Function for generating convex fuzzy measures

fm.get_num_tuples

Function for exporting number of tuples

fm.Banzhaf2addMob

Function for calculating Banzhaf values of 2-additive fuzzy measure in Mobius representation

Choquet integral computation function

fm.ConvertCoMob2Kinter

Function for dual k-interactive fuzzy measure from Mobius to standard representation

Banzhaf value computation function in Mobius representation

fm.EntropyChoquet

Entropy of fuzzy measure

fm.EntropyChoquetMob

Entropy Choquet computation function in Mobius representation

fm.ChoquetCoMobKInter

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

Banzhaf value computation function

fm.BanzhafMob_sparse

Banzhaf values computation function in sparse representation

fm.ConstructLambdaMeasure

Function for Constructing Lambda

fm.ChoquetKinter

Choquet integral value computation function in standard representation wrt k-interactive fuzzy measure

Bipartition interaction index computation function

fm.BipartitionBanzhaf

Bipartition Banhzaf interaction index computation function

fm.Choquet2addMob

Function for calculating Choquet integral value for 2-additive fuzzy measure in Mobius representation

fm.FuzzyMeasureFitLPMob

Mobius Fuzzy Measure Fitting function, R wrapper for FuzzyMeasureFitLP() in fuzzymeasurefit.cpp

fm.ConstructLambdaMeasureMob

Function for Constructing Lambda in Mobius representation

Initialisation function

fm.FuzzyMeasureFitLP

Fuzzy Measure Fitting function.