Rfmtool package

Description

This function shows a list of function included in this toolbox

Usage

fm()

Details

The following functions involve the parameters v (the array containing the fuzzy measure in standard representation) or Mob (in Mobius representation), n - the dimension and m = 2^n. The values of the fuzzy measure always obey the binary ordering.

Author(s)

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

Examples

fm()

Banzhaf value computation function

Description

Calculates the Banzhaf indices of input criteria from general fuzzy measure.

Usage

fm.Banzhaf(v,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.Banzhaf(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)

env<-fm.Free(env)

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

Description

Calculate the Banzhaf values of a 2-additive fuzzy measure for n inputs given in Mobius representation. The results are in arrays.

Usage

  fm.Banzhaf2addMob(n, Mob)

Arguments

Value

Author(s)

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

Examples

  Banzhaf  <- fm.Banzhaf2addMob(3, c(0.2, 0.3, 0.5, -0.2, 0.4, 0.1))
  

Banzhaf value computation function in Mobius representation

Description

Calculates the Banzhaf indices of input criteria from general fuzzy measure in Mobius representation.

Usage

fm.BanzhafMob(Mob,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.BanzhafMob(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)
env<-fm.Free(env)

Banzhaf values computation function in sparse representation

Description

Calculates Banzhaf values vectors of size n of a sparse fuzzy measure

Usage

  fm.BanzhafMob_sparse(n, envsp=NULL)

Arguments

Value

Author(s)

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

Examples

    n <- 3
  tups<-vector()
  tupsidx<-vector()
  envsp <- fm.PrepareSparseFM(n, tups,tupsidx) 
    envsp <- fm.add_singletons_sparse(c(0.2,0.1,0.2),envsp) 
    envsp <- fm.add_pair_sparse(1,2,0.4,envsp);

    fm.BanzhafMob_sparse(3, envsp)

    envsp <- fm.FreeSparseFM(envsp)
  

Bipartition interaction index computation function

Description

Calculates the Bipartition interaction indices of input criteria from general fuzzy measure.

Usage

fm.Bipartition(v,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.Bipartition(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)
env<-fm.Free(env)

Bipartition Banhzaf interaction index computation function

Description

Calculates the Banzhaf Bipartition interaction indices of input criteria from general fuzzy measure.

Usage

fm.BipartitionBanzhaf(v,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.BipartitionBanzhaf(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)
env<-fm.Free(env)

Choquet integral computation function

Description

Calculates the value of a discrete Choquet integral of input x, with fuzzy measure in general representation.

Usage

fm.Choquet(x, v, env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.Choquet(c(0.6, 0.3, 0.8), c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)
env<-fm.Free(env)

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

Description

Calculates the Choquet integral value of a 2-additive fuzzy measure for n inputs given in Mobius representation.

Usage

  fm.Choquet2addMob(n, x, Mob)

Arguments

Value

Author(s)

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

Examples

 
  Choquet <- fm.Choquet2addMob(3, c(0.2,0.5,0.4), c(0.2, 0.3, 0.5, -0.2, 0.4, 0.1))
  

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)

Arguments

Value

Author(s)

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)
  

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

Description

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

Usage

fm.ChoquetKinter(x, v, kint, env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.ChoquetKinter(c(0.6,0.3,0.8),c(0,0.3,0.5,0.6,0.4,0.8,0.7,1),2,env)
env<-fm.Free(env)

Choquet integral value computation function in Mobius representation

Description

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

Usage

fm.ChoquetMob(x, Mob, env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.ChoquetMob(c(0.2,0.5,0.4), c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)

Choquet integral computation function in sparse representation

Description

Calculates the Choquet integral in Mobius sparse representation.

Usage

  fm.ChoquetMob_sparse(x, envsp=NULL)

Arguments

Value

Author(s)

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

Examples

  n <- 3
  envsp <- fm.PrepareSparseFM(n, vector(), vector()) 
  envsp <- fm.add_singletons_sparse(c(0.2,0.1,0.2),envsp) 
  envsp <- fm.add_pair_sparse(1,2,0.4,envsp);

   ChoquetMobsparse <- fm.ChoquetMob_sparse(c(0.1,0.05,0.2),envsp)
   ChoquetMobsparse 
   envsp <- fm.FreeSparseFM(envsp)
  

Function for Constructing Lambda

Description

Finds the value of lambda and calculates the rest of the values of the fuzzy measure, given its values at singletons; singletons is an array of size n. The outputs are lambda and v, v is in standard representation and binary ordering.

Usage

fm.ConstructLambdaMeasure(singletons,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
w <- fm.ConstructLambdaMeasure(c(0, 0.3, 0.5),env)
 

Function for Constructing Lambda in Mobius representation

Description

Finds the value of lambda and calculates the rest of the values of the fuzzy measure, given its values at singletons; singletons is an array of size n. The outputs are lambda and measure, measure is in Mobius representation.

Usage

fm.ConstructLambdaMeasureMob(singletons,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
w <- fm.ConstructLambdaMeasureMob(c(0, 0.3, 0.5),env)
w$measure 
fm.Free(env)

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

Description

Converts dual k-interactive fuzzy measure from Mobius to standard representation.

Usage

fm.ConvertCoMob2Kinter(Mob,kadd, fullmu, env=NULL)

Arguments

Value

Author(s)

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

Examples

env <-fm.Init(4)
fullmu <- 0
step<-0.001
Fn <- NULL
        fuzzymeasures <- fm.generate_fm_kinteractivedualconvex(1, 4, 2, 1000,
        step, Fn, env)

fm.ConvertCoMob2Kinter(fuzzymeasures$V, 2, fullmu, env )
  

Entropy of fuzzy measure

Description

Calculates entropy value of the Choquet integral for the fuzzy measure v in general representation

Usage

fm.EntropyChoquet(v,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.EntropyChoquet(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1))

Entropy Choquet computation function in Mobius representation

Description

Calculates entropy value of the Choquet integral for the fuzzy measure v in Mobius representation

Usage

fm.EntropyChoquetMob(Mob,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.EntropyChoquetMob(c(0.0,0.3,0.5,-0.2,0.4,0.1,-0.2,0.1),env)

FreeSparseFM function

Description

Frees the memory previously allocated in env.

Usage

  fm.Free(env)

Arguments

Value

Author(s)

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

Examples

     n<-3
    env <- fm.Init(n)
    env<-fm.Free(env)
    env

  

FreeSparseFM function

Description

Frees the memory previously allocated in envsp.

Usage

  fm.FreeSparseFM(envsp)

Arguments

Value

Author(s)

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

Examples

     n<-3
    envsp <- fm.PrepareSparseFM(n, vector(), vector()) 
    envsp <- fm.FreeSparseFM(envsp)
    envsp <- fm.PrepareSparseFM(n, c(0.2,0.4,0.1), c(2,1,2,2,1,3,3,1,2,3)) 
     envsp <- fm.FreeSparseFM(envsp) 
envsp
  

Fuzzy Measure Fitting function.

Description

Estimate values of the fuzzy measures from empirical data. The result is an array containing the values of a standard fuzzy measure in binary ordering. kadd defines the complexity of fuzzy measure. If kadd is not provided, its default value is equal to the number of inputs.

Usage

fm.FuzzyMeasureFitLP(data, env=NULL, kadd="NA", 
        options=0, indexlow=(NULL), indexhigh=(NULL) , option1=0, orness=(NULL))

Arguments

Value

Note

The fit might not be perfect, and not all the constraints can be fully met.

Author(s)

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

Examples

d <-  matrix( c( 0.00125122, 0.563568, 0.193298, 0.164338, 
            0.808716, 0.584991, 0.479858, 0.544309, 
            0.350281, 0.895935, 0.822815, 0.625868, 
            0.746582, 0.174103, 0.858917, 0.480347, 
            0.71048, 0.513519, 0.303986, 0.387631, 
            0.0149841, 0.0914001, 0.364441, 0.134229, 
            0.147308, 0.165894, 0.988495, 0.388044, 
            0.445679, 0.11908, 0.00466919, 0.0897714, 
            0.00891113, 0.377869, 0.531647, 0.258585, 
            0.571167, 0.601746, 0.607147, 0.589803, 
            0.166229, 0.663025, 0.450775, 0.357412, 
            0.352112, 0.0570374, 0.607666, 0.270228, 
            0.783295, 0.802582, 0.519867, 0.583348, 
            0.301941, 0.875946, 0.726654, 0.562174, 
            0.955872, 0.92569, 0.539337, 0.633631, 
            0.142334, 0.462067, 0.235321, 0.228419, 
            0.862213, 0.209595, 0.779633, 0.498077, 
            0.843628, 0.996765, 0.999664, 0.930197, 
            0.611481, 0.92426, 0.266205, 0.334666, 
            0.297272, 0.840118, 0.0237427, 0.168081), 
       nrow=20, 
       ncol=4,byrow=TRUE);
env<-fm.Init(3)
fm.FuzzyMeasureFitLP(d,env)
indexlow=c(0.1,0.1,0.2);
indexhigh=c(0.9,0.9,0.5);
fm.FuzzyMeasureFitLP(d,env, kadd=2, indexlow, indexhigh, 
  options=3, option1=1, orness=c(0.1,0.7))
  

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

Description

Estimate values of the Mobius fuzzy measures from empirical data. The result is an array containing the values of the fuzzy measure in Mobius, ordered according to set cardinalities. kadd defines the complexity of fuzzy measure. if kadd is not provided, its default value is equal to the number of inputs.

Usage

fm.FuzzyMeasureFitLPMob(data, env=NULL, kadd="NA", 
        options=0, indexlow=(NULL), indexhigh=(NULL) , option1=0, orness=(NULL))

Arguments

Value

Note

The fit might not be perfect, and not all the constraints can be fully met.

Author(s)

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

Examples

d <-  matrix( c( 0.00125122, 0.563568, 0.193298, 0.164338, 
            0.808716, 0.584991, 0.479858, 0.544309, 
            0.350281, 0.895935, 0.822815, 0.625868, 
            0.746582, 0.174103, 0.858917, 0.480347, 
            0.71048, 0.513519, 0.303986, 0.387631, 
            0.0149841, 0.0914001, 0.364441, 0.134229, 
            0.147308, 0.165894, 0.988495, 0.388044, 
            0.445679, 0.11908, 0.00466919, 0.0897714, 
            0.00891113, 0.377869, 0.531647, 0.258585, 
            0.571167, 0.601746, 0.607147, 0.589803, 
            0.166229, 0.663025, 0.450775, 0.357412, 
            0.352112, 0.0570374, 0.607666, 0.270228, 
            0.783295, 0.802582, 0.519867, 0.583348, 
            0.301941, 0.875946, 0.726654, 0.562174, 
            0.955872, 0.92569, 0.539337, 0.633631, 
            0.142334, 0.462067, 0.235321, 0.228419, 
            0.862213, 0.209595, 0.779633, 0.498077, 
            0.843628, 0.996765, 0.999664, 0.930197, 
            0.611481, 0.92426, 0.266205, 0.334666, 
            0.297272, 0.840118, 0.0237427, 0.168081), 
       nrow=20, 
       ncol=4,byrow=TRUE);
env<-fm.Init(3)
fm.FuzzyMeasureFitLPMob(d,env)
indexlow=c(0.1,0.1,0.2);
indexhigh=c(0.9,0.9,0.5);
fm.FuzzyMeasureFitLPMob(d,env, kadd=2, indexlow, indexhigh, 
  options=3, option1=1, orness=c(0.1,0.7))
  

Initialisation function

Description

This function initialises the internal structures which makes computations faster. The structures are saved in the output environment variable, which should be subsequently passed to other functions. Several environment variables (for different dimensions) can be initialised at the same time.

Usage

fm.Init(n1)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)

Interaction Index computation function

Description

Calculates all the interaction indices of input criteria for standard fuzzy measure.

Usage

fm.Interaction(v,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.Interaction(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)

Banzhaf Interaction Index computation function

Description

Calculates all the Banzhaf Interaction indices of input criteria for a standard fuzzy measure.

Usage

fm.InteractionB(v,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.InteractionB(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)

Banzhaf InteractionB Index computation function in Mobius representation

Description

Calculates all the Banzhaf InteractionB indices of input criteria for a Mobius fuzzy measure.

Usage

fm.InteractionBMob(Mob,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.InteractionBMob(c( 0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)

Interaction Index computation function for Mobius fuzzy measure

Description

Calculates all the interaction indices of input criteria for a Mobius fuzzy measure.

Usage

fm.InteractionMob(Mob,env )

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.InteractionMob(c( 0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)

IsMeasureAdditive function

Description

Returns 1 if yes, 0 if no; v is a fuzzy measure in standard representation.

Usage

fm.IsMeasureAdditive(v,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureAdditive(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)
 

IsMeasureAdditive function in Mobius representation

Description

Returns 1 if yes, 0 if no; v is a fuzzy measure in Mobius representation.

Usage

fm.IsMeasureAdditiveMob(Mob,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureAdditiveMob(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)

IsMeasureBalanced function

Description

Returns 1 if yes, 0 if no; v is a fuzzy measure in standard representation.

Usage

fm.IsMeasureBalanced(v,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureBalanced(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)

IsMeasureBalanced function in Mobius representation

Description

Returns 1 if yes, 0 if no; Mob is a fuzzy measure in Mobius representation.

Usage

fm.IsMeasureBalancedMob(Mob,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureBalancedMob(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)
 

IsMeasureKmaxitive function

Description

Returns k; v is a fuzzy measure in standard representation.

Usage

fm.IsMeasureKmaxitive(v,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureKmaxitive(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)

IsMeasureKmaxitive function in Mobius representation

Description

Returns k; mob is a fuzzy measure in Mobius representation.

Usage

fm.IsMeasureKmaxitiveMob(Mob,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureKmaxitiveMob(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)

IsMeasureSelfdual function

Description

Returns 1 if yes, 0 if no; v is a fuzzy measure in standard representation.

Usage

fm.IsMeasureSelfdual(v,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureSelfdual(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)

IsMeasureSelfdual function in Mobius representation

Description

Returns 1 if yes, 0 if no; Mob is a fuzzy measure in Mobius representation.

Usage

fm.IsMeasureSelfdualMob(Mob,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureSelfdualMob(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)

IsMeasureSub additive function

Description

Returns 1 if yes, 0 if no; v is a fuzzy measure in standard representation.

Usage

fm.IsMeasureSubadditive(v,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureSubadditive(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)
 

IsMeasureSub additive function in Mobius representation

Description

Returns 1 if yes, 0 if no; v is a fuzzy measure in Mobius representation.

Usage

fm.IsMeasureSubadditiveMob(Mob,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureSubadditiveMob(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)

IsMeasureSub modular function

Description

Returns 1 if yes, 0 if no; v is a fuzzy measure in standard representation.

Usage

fm.IsMeasureSubmodular(v,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureSubmodular(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)

IsMeasureSubmodular function in Mobius representation

Description

Returns 1 if yes, 0 if no; Mob is a fuzzy measure in Mobius representation.

Usage

fm.IsMeasureSubmodularMob(Mob,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureSubmodularMob(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)
 

IsMeasureSuperadditive function

Description

Returns 1 if yes, 0 if no; v is a fuzzy measure in standard representation.

Usage

fm.IsMeasureSuperadditive(v,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureSuperadditive(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)
 

IsMeasureSuperadditive function in Mobius representation

Description

Returns 1 if yes, 0 if no; Mob is a fuzzy measure in Mobius representation.

Usage

fm.IsMeasureSuperadditiveMob(Mob,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureSuperadditiveMob(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)
  

IsMeasureSupermodular function

Description

Returns 1 if yes, 0 if no; v is a fuzzy measure in standard representation.

Usage

fm.IsMeasureSupermodular(v,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureSupermodular(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)

IsMeasureSupermodular function in Mobius representation

Description

Returns 1 if yes, 0 if no; Mob is a fuzzy measure in Mobius representation.

Usage

fm.IsMeasureSupermodularMob(Mob,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureSupermodularMob(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)

IsMeasureSymmetric function

Description

Returns 1 if yes, 0 if no; v is a fuzzy measure in standard representation.

Usage

fm.IsMeasureSymmetric(v,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureSymmetric(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)

IsMeasureSymmetric function in Mobius representation

Description

Returns 1 if yes, 0 if no; v is a fuzzy measure in Mobius representation.

Usage

fm.IsMeasureSymmetricMob(Mob,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.IsMeasureSymmetricMob(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)

Mobius transform function

Description

Calculates Mobius representation of general fuzzy measure, the input and output is an array of size 2^n=m in binary ordering.

Usage

fm.Mobius(v,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.Mobius(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)

Nonadditivity index computation function

Description

Calculate the nonadditivity indices of input criteria from general fuzzy measure.

Usage

fm.NonadditivityIndex(v,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.NonadditivityIndex(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)

Nonadditivity index computation function in Mobius representation

Description

Calculate the nonadditivity indices of input criteria from general fuzzy measure in Mobius representation.

Usage

  fm.NonadditivityIndexMob(Mob,env=NULL)

Arguments

Value

Author(s)

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

Examples

  env<-fm.Init(3)
  NonadditivityIndex <- fm.NonadditivityIndexMob(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)
  

Nonmodularity index computation function

Description

Calculate all the m = 2^n nonmodularity indices of fuzzy measure v given in standard representation

Usage

  fm.NonmodularityIndex(v, env = NULL)

Arguments

Value

Author(s)

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

Examples

 
env<-fm.Init(3)
Nonmodularityindex <- fm.NonmodularityIndex(c(0,0.3,0.5,0.6,0.4,0.8,0.7,1),env)
  

NonmodularityIndexKinteractive computation function

Description

Calculate all the m = 2^n nonmodularity indices of k-interactive fuzzy measure v given in standard representation (in cardinality ordering)

Usage

  fm.NonmodularityIndexKinteractive(v, env = NULL, kadd = "NA")

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(3)
  fm.NonmodularityIndexKinteractive(c(0,0.3,0.5,0.6,0.4,0.8,0.7,1),env,2)
  

Nonmodularityindex computation function in Mobius representation

Description

Calculates all the nonmodularity indices of fuzzy measure in Mobius representation representation

Usage

  fm.NonmodularityIndexMob(Mob, env = NULL)

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(3)
  fm.NonmodularityIndexMob(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)
  

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

Description

Calculate all the m = 2^n nonmodularity indices of k-additive in Mobius representation(in cardinality ordering)

Usage

  fm.NonmodularityIndexMobkadditive(Mob, env = NULL, kadd = "NA")

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(3)
  fm.NonmodularityIndexMobkadditive(c(0.0,0.3,0.5,-0.2,0.4,0.1,-0.2,0.1),env,2)
  

Nonmodularity index computation function in sparse representation

Description

Calculate all 2^n nonmodularity indices using Mobius transform of a fuzzy measure of lenght 2^n=m, using sparse representation

Usage

  fm.NonmodularityIndex_sparse( n, envsp=NULL)

Arguments

Value

Author(s)

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

Examples

    n <- 3
    tups<-vector()
    tupsidx<-vector()
    envsp <- fm.PrepareSparseFM(n, tups,tupsidx) 
    envsp <- fm.add_singletons_sparse(c(0.2,0.1,0.2),envsp) 
    envsp <- fm.add_pair_sparse(1,2,0.4,envsp);

    fm.NonmodularityIndex_sparse(3,envsp)
    envsp <- fm.FreeSparseFM(envsp)
  

OrnessChoquet function

Description

Calculate Orness value of the Choquet integral of the fuzzy measure, where v is a standard representation.

Usage

fm.OrnessChoquet(v,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.OrnessChoquet(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)
 

OrnessChoquet function in Mobius representation

Description

Calculate Orness value of the Choquet integral of the fuzzy measure, where Mob is the Mobius representation.

Usage

fm.OrnessChoquetMob(Mob,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.OrnessChoquetMob(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)

PrepareSparseFM preparation function

Description

This function initialises Sparse representation structure. It is used to allocate storage and later populate these values

Usage

  fm.PrepareSparseFM(n, tups, tupsidx)

Arguments

Value

Author(s)

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

Examples

   n<-3
    envsp <- fm.PrepareSparseFM(n, vector(), vector()) 
    envsp <- fm.FreeSparseFM(envsp)
    envsp <- fm.PrepareSparseFM(n, c(0.2,0.4,0.1), c(2,1,2,2,1,3,3,1,2,3)) 
envsp
     envsp <- fm.FreeSparseFM(envsp) 

Shapley value computation function

Description

Calculates the Shapley values of input criteria from general fuzzy measure,

Usage

fm.Shapley(v,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.Shapley(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)

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

Description

Calculate the Shapley values of a 2-additive fuzzy measure for n inputs given in Mobius representation. The results are in arrays.

Usage

  fm.Shapley2addMob(n, Mob)

Arguments

Value

Author(s)

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

Examples

   Shapley <- fm.Shapley2addMob(3, c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1))
  

Shapley value computation function in Mobius representation

Description

Calculate the Shapley indices of input criteria from general fuzzy measure in Mobius representation.

Usage

fm.ShapleyMob(Mob,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.ShapleyMob(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)

Shapley values computation function in sparse representation

Description

Calculate Shapley values vectors of size n of a sparse fuzzy measure

Usage

  fm.ShapleyMob_sparse(n, envsp=NULL)

Arguments

Value

Author(s)

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

Examples

    n <- 3
    envsp <- fm.PrepareSparseFM(n, c(0.2,0.4,0.1), c(2,1,2,2,1,3,3,1,2,3)) 

   fm.ShapleyMob_sparse(3, envsp)

   envsp <- fm.FreeSparseFM(envsp) 
    
  

Show Coalitions function

Description

Return the decimal expression for the subsets A. In binary and in cardinality ordering respectively.

Usage

  fm.ShowCoalitions(env = NULL)

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(3)
  ShowCoalitions <- fm.ShowCoalitions(env)
  ShowCoalitions 
  

Show CoalitionsCard function

Description

Return the decimal expression for the subsets A. In binary and in cardinality ordering respectively.

Usage

  fm.ShowCoalitionsCard(env = NULL)

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(3)
  CoalitionsCard <- fm.ShowCoalitionsCard(env)
  CoalitionsCard 
  

Sugeno computation function

Description

Calculate the value of a Sugeno integral of input x, with fuzzy measure in standard representation

Usage

fm.Sugeno(x, v,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.Sugeno(c(0.6, 0.3, 0.8), c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env) 

Sugeno function in Mobius representation

Description

Calculate the value of a Sugeno integral of input x, with fuzzy measure in mobius representation

Usage

fm.SugenoMob(x, Mob,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.SugenoMob(c(0.6, 0.3, 0.8), c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)

Zeta transform function

Description

Calculate the general fuzzy measure from Mobius representation. The input and output is an array of size 2^n=m in binary ordering. This is the inverse of the Mobius function.

Usage

fm.Zeta(Mob,env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.Zeta(c(0.0,0.3,0.5,-0.2,0.4,0.1,-0.2,0.1),env)

Function for adding a pair to the sparse fuzzy measure

Description

This is used for populating capacities which Add a pair v_ij to the structure, their Indices are 1-based.

Usage

  fm.add_pair_sparse( i, j, v, envsp = NULL)

Arguments

Value

Author(s)

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

Examples

  n <- 3
  tups<-vector()
  tupsidx<-vector()
  envsp <- fm.PrepareSparseFM(n, tups,tupsidx) 
   envsp <-fm.add_pair_sparse(1,2, 0.4, envsp)
   envsp <-fm.add_pair_sparse(1,3, 0.3, envsp)
envsp
     envsp <- fm.FreeSparseFM(envsp)    
  

Function for adding singletons to the sparse fuzzy measure

Description

This is used for adding singletons to the structure.

Usage

  fm.add_singletons_sparse(v, envsp=NULL)

Arguments

Value

Author(s)

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

Examples

  n <- 3
  tups<-vector()
  tupsidx<-vector()
  envsp <- fm.PrepareSparseFM(n, tups,tupsidx) 

 envsp <- fm.add_singletons_sparse(c(0, 0.3, 0.5),envsp)
  

Function for adding singletons to the sparse fuzzy measure

Description

This is used for populating capacities which Add a tuple of size tupsize to the structure whose Indices are 1-based in tuple.

For populating capacities, adds a whose 1-based indices are in tuple

Usage

  fm.add_tuple_sparse( tuple, v, envsp=NULL)

Arguments

Value

Author(s)

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

Examples

    n <- 4
  tups<-vector()
  tupsidx<-vector()
  envsp <- fm.PrepareSparseFM(n, tups,tupsidx) 
  envsp <- fm.add_tuple_sparse(c(1,2,3),0.2,envsp)
  envsp <- fm.add_tuple_sparse(c(1,3,4),0.3,envsp)
  

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

Description

Checks supermodularity of the set function v in Mobius representation using stan- dard check.

Usage

  fm.check_convexity_monotonicity_mob(v, len, env=NULL)

Arguments

Value

Author(s)

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

Examples

 
env<-fm.Init(3)
step <- 0.001
Fn <- NULL
Option<- 3
fuzzymeasures <- fm.generate_fm_randomwalk(1, 3, 2, 1000, Option, step, Fn, env)
len <- fuzzymeasures$length
check <- fm.check_convexity_monotonicity_mob(fuzzymeasures$V, len, env)

Function for checking monotonicity of the set function v

Description

Checks monotonicity of the set function v in standard representation using insert sort.

Usage

  fm.check_monotonicity(v, env=NULL)

Arguments

Value

Author(s)

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

Examples

 
env<-fm.Init(3)
v <- fm.generate_fm_sorting(1, 1000, 0, env)
monotonicity <- fm.check_monotonicity(v, env)

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

Description

Checks monotonicity of the set function v in Mobius representation using standard check.

Usage

  fm.check_monotonicity_mob(v, len, env=NULL)

Arguments

Value

Author(s)

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

Examples

 
env<-fm.Init(3)
step <- 100
Fn <- NULL
Option<- 3
fuzzymeasures <- fm.generate_fm_randomwalk(1, 3, 2, 1000, Option, step, Fn, env)
len <- fuzzymeasures$length
check <- fm.check_monotonicity_mob(fuzzymeasures$V, len, env)
check

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

Description

Check the monotonicity of the 2-additive set function v in Mobius representation using fast check.

Usage

  fm.check_monotonicity_mob_2additive(v, n, temp=NULL)

Arguments

Value

Author(s)

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

Examples

 
  v <- fm.generate_fm_2additive(1, 10)
  n <- 10
  v$len
  v$V
  check <- fm.check_monotonicity_mob_2additive(v$V, n)
  check

  temp <- array(0.0,10*10);
  check <- fm.check_monotonicity_mob_2additive(v$V, n, temp)
  check

Function for checking monotonicity of the set function v

Description

Checks monotonicity of the set function v in standard representation using insert sort.

Usage

  fm.check_monotonicity_sort_insert(v, indices, env=NULL)

Arguments

Value

Author(s)

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

Examples

 
 env<-fm.Init(3)
 v <- fm.generate_fm_sorting(1, 1000, 0, env)
  out <- fm.check_monotonicity_sort_merge(v, NULL, env)
  out$V[1] = out$V[1] *1.1
  out<- fm.check_monotonicity_sort_insert(out$V, out$index, env)
  out$out

Function for checking monotonicity of the set function v

Description

Checks monotonicity of the set function v in standard representation using merge sort.

Usage

  fm.check_monotonicity_sort_merge(v, indices=NULL, env=NULL)

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(3)
  v <- fm.generate_fm_sorting(1, 1000, 0, env)
  v
  measure <- fm.check_monotonicity_sort_merge(v,NULL, env)

  print(measure$out)
  
    measure$V[1] = measure$V[1] *1.1
    measure <- fm.check_monotonicity_sort_merge(measure$V, measure$index, env)

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

Description

Calculates the dual of a k-additive fuzzy measures for n inputs.

Usage

  fm.dualMobKadd(Mob, env = NULL, kadd = "NA")

Arguments

Value

Author(s)

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

Examples

 
env<-fm.Init(3)
  dualMob_Kadd <- fm.dualMobKadd(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1), env,2)
  

Function for calculating dual of fuzzy measure

Description

Calculates the dual of fuzzy measure v, returns it as value of the function (array of size m).

Usage

fm.dualm(v, env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
w <- fm.dualm(c(0, 0.3, 0.5, 0.6, 0.4, 0.8, 0.7, 1),env)
 

Dualm computation function in Mobius representation

Description

Calculates the dual of fuzzy measure v, returns it as value of the function (array of size m).

Usage

fm.dualmMob(Mob,env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
w <- fm.dualmMob(c(0.0, 0.3, 0.5, -0.2, 0.4, 0.1, -0.2, 0.1),env)
  

Basic error check

Description

This function checks that the enviromnemt variable is internally consistent.

Usage

fm.errorcheck(env)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
fm.errorcheck(env)

Function for exporting full representation of 2-additive capacity

Description

From sparse to full representation of 2-additive capacity (singletons and pairs, augmented with 0s).

Usage

  fm.expand_2add_full(n, envsp=NULL)

Arguments

Value

Author(s)

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

Examples

  n <- 3
  envsp <- fm.PrepareSparseFM(n, vector(), vector()) 
  envsp <- fm.add_singletons_sparse(c(0.2,0.1,0.2),envsp) 
  envsp <- fm.add_pair_sparse(1,2,0.4,envsp);

  cap2add <- fm.expand_2add_full(n,envsp)
  cap2add 

  envsp <- fm.FreeSparseFM(envsp)

Function for exporting full capacity from sparse representation

Description

Exports from sparse to full capacity.

Usage

  fm.expand_sparse_full(n, envsp=NULL)

Arguments

Value

Author(s)

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

Examples

  n<-3
  envsp <- fm.PrepareSparseFM(n, vector(), vector()) 
  envsp <- fm.add_singletons_sparse(c(0.2,0.1,0.2),envsp) 
  envsp <- fm.add_pair_sparse(1,2,0.4,envsp);

  cap <- fm.expand_sparse_full(n, envsp)
  cap 

  envsp <- fm.FreeSparseFM(envsp)
  

Function for exporting maximal chains

Description

Returns in mc the arrays of maximal chains (there are n! such arrays) of a fuzzy measure v. Each maximal chain corresponds to the coefficients of a linea. function on the respective simplex

Usage

  fm.export_maximal_chains(v, env = NULL)

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(3)
  exportmaximalchains <- fm.export_maximal_chains(
   c(0, 0.00224, 0.0649, 0.510, 0.00965, 0.374,0.154, 1),env)
  

Fuzzy Measure Fitting function

Description

Estimate values of the fuzzy measures from empirical data.

Usage

fm.fitting(data, env=NULL, kadd="NA")

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
d <-  matrix( c( 0.00125122, 0.563568, 0.193298, 0.164338, 
            0.808716, 0.584991, 0.479858, 0.544309, 
            0.350281, 0.895935, 0.822815, 0.625868, 
            0.746582, 0.174103, 0.858917, 0.480347, 
            0.71048, 0.513519, 0.303986, 0.387631, 
            0.0149841, 0.0914001, 0.364441, 0.134229, 
            0.147308, 0.165894, 0.988495, 0.388044, 
            0.445679, 0.11908, 0.00466919, 0.0897714, 
            0.00891113, 0.377869, 0.531647, 0.258585, 
            0.571167, 0.601746, 0.607147, 0.589803, 
            0.166229, 0.663025, 0.450775, 0.357412, 
            0.352112, 0.0570374, 0.607666, 0.270228, 
            0.783295, 0.802582, 0.519867, 0.583348, 
            0.301941, 0.875946, 0.726654, 0.562174, 
            0.955872, 0.92569, 0.539337, 0.633631, 
            0.142334, 0.462067, 0.235321, 0.228419, 
            0.862213, 0.209595, 0.779633, 0.498077, 
            0.843628, 0.996765, 0.999664, 0.930197, 
            0.611481, 0.92426, 0.266205, 0.334666, 
            0.297272, 0.840118, 0.0237427, 0.168081), 
       nrow=20, 
       ncol=4,byrow=TRUE);
fm.fitting(d,env)
  

Fuzzy Measure Fitting function

Description

Estimate values of the fuzzy measures from empirical data tailored 2-additive standard fuzzy measure.

Usage

fm.fitting2additive(data, options=0, indexlow, indexhigh , option1=0, orness)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
d <-  matrix( c( 0.00125122, 0.563568, 0.193298, 0.164338, 
            0.808716, 0.584991, 0.479858, 0.544309, 
            0.350281, 0.895935, 0.822815, 0.625868, 
            0.746582, 0.174103, 0.858917, 0.480347, 
            0.71048, 0.513519, 0.303986, 0.387631, 
            0.0149841, 0.0914001, 0.364441, 0.134229, 
            0.147308, 0.165894, 0.988495, 0.388044, 
            0.445679, 0.11908, 0.00466919, 0.0897714, 
            0.00891113, 0.377869, 0.531647, 0.258585, 
            0.571167, 0.601746, 0.607147, 0.589803, 
            0.166229, 0.663025, 0.450775, 0.357412, 
            0.352112, 0.0570374, 0.607666, 0.270228, 
            0.783295, 0.802582, 0.519867, 0.583348, 
            0.301941, 0.875946, 0.726654, 0.562174, 
            0.955872, 0.92569, 0.539337, 0.633631, 
            0.142334, 0.462067, 0.235321, 0.228419, 
            0.862213, 0.209595, 0.779633, 0.498077, 
            0.843628, 0.996765, 0.999664, 0.930197, 
            0.611481, 0.92426, 0.266205, 0.334666, 
            0.297272, 0.840118, 0.0237427, 0.168081), 
       nrow=20, 
       ncol=4,byrow=TRUE);
       
    

indexlow=c(0.1,0.1,0.2);
indexhigh=c(0.9,0.9,0.5);

fm.fitting2additive(d, options=3, indexlow, indexhigh, option1=0, orness=c(0.1,0.7))
  

Fuzzy Measure Fitting function

Description

Estimate values of the k-interacive fuzzy measures from empirical data.

Usage

fm.fittingKinteractive(data, env=NULL, kadd="NA", K="NA")

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
d <-  matrix( c( 0.00125122, 0.563568, 0.193298, 0.164338, 
            0.808716, 0.584991, 0.479858, 0.544309, 
            0.350281, 0.895935, 0.822815, 0.625868, 
            0.746582, 0.174103, 0.858917, 0.480347, 
            0.71048, 0.513519, 0.303986, 0.387631, 
            0.0149841, 0.0914001, 0.364441, 0.134229, 
            0.147308, 0.165894, 0.988495, 0.388044, 
            0.445679, 0.11908, 0.00466919, 0.0897714, 
            0.00891113, 0.377869, 0.531647, 0.258585, 
            0.571167, 0.601746, 0.607147, 0.589803, 
            0.166229, 0.663025, 0.450775, 0.357412, 
            0.352112, 0.0570374, 0.607666, 0.270228, 
            0.783295, 0.802582, 0.519867, 0.583348, 
            0.301941, 0.875946, 0.726654, 0.562174, 
            0.955872, 0.92569, 0.539337, 0.633631, 
            0.142334, 0.462067, 0.235321, 0.228419, 
            0.862213, 0.209595, 0.779633, 0.498077, 
            0.843628, 0.996765, 0.999664, 0.930197, 
            0.611481, 0.92426, 0.266205, 0.334666, 
            0.297272, 0.840118, 0.0237427, 0.168081), 
       nrow=20, 
       ncol=4,byrow=TRUE);
fm.fittingKinteractive(d,env,2,0.8)
  

Fuzzy Measure Fitting function of the k-interactive

Description

Estimate values of the k-interacive fuzzy measures from empirical data.

Usage

fm.fittingKinteractiveAuto(data, env=NULL, kadd="NA")

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
d <-  matrix( c( 0.00125122, 0.563568, 0.193298, 0.164338, 
            0.808716, 0.584991, 0.479858, 0.544309, 
            0.350281, 0.895935, 0.822815, 0.625868, 
            0.746582, 0.174103, 0.858917, 0.480347, 
            0.71048, 0.513519, 0.303986, 0.387631, 
            0.0149841, 0.0914001, 0.364441, 0.134229, 
            0.147308, 0.165894, 0.988495, 0.388044, 
            0.445679, 0.11908, 0.00466919, 0.0897714, 
            0.00891113, 0.377869, 0.531647, 0.258585, 
            0.571167, 0.601746, 0.607147, 0.589803, 
            0.166229, 0.663025, 0.450775, 0.357412, 
            0.352112, 0.0570374, 0.607666, 0.270228, 
            0.783295, 0.802582, 0.519867, 0.583348, 
            0.301941, 0.875946, 0.726654, 0.562174, 
            0.955872, 0.92569, 0.539337, 0.633631, 
            0.142334, 0.462067, 0.235321, 0.228419, 
            0.862213, 0.209595, 0.779633, 0.498077, 
            0.843628, 0.996765, 0.999664, 0.930197, 
            0.611481, 0.92426, 0.266205, 0.334666, 
            0.297272, 0.840118, 0.0237427, 0.168081), 
       nrow=20, 
       ncol=4,byrow=TRUE);
fm.fittingKinteractiveAuto(d,env,2)
  

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

Description

Estimate values of the k-interacive fuzzy measures from empirical data using maximal chains method.

Usage

fm.fittingKinteractiveMC(data, env=NULL, kadd="NA", K="NA")

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
d <-  matrix( c( 0.00125122, 0.563568, 0.193298, 0.164338, 
            0.808716, 0.584991, 0.479858, 0.544309, 
            0.350281, 0.895935, 0.822815, 0.625868, 
            0.746582, 0.174103, 0.858917, 0.480347, 
            0.71048, 0.513519, 0.303986, 0.387631, 
            0.0149841, 0.0914001, 0.364441, 0.134229, 
            0.147308, 0.165894, 0.988495, 0.388044, 
            0.445679, 0.11908, 0.00466919, 0.0897714, 
            0.00891113, 0.377869, 0.531647, 0.258585, 
            0.571167, 0.601746, 0.607147, 0.589803, 
            0.166229, 0.663025, 0.450775, 0.357412, 
            0.352112, 0.0570374, 0.607666, 0.270228, 
            0.783295, 0.802582, 0.519867, 0.583348, 
            0.301941, 0.875946, 0.726654, 0.562174, 
            0.955872, 0.92569, 0.539337, 0.633631, 
            0.142334, 0.462067, 0.235321, 0.228419, 
            0.862213, 0.209595, 0.779633, 0.498077, 
            0.843628, 0.996765, 0.999664, 0.930197, 
            0.611481, 0.92426, 0.266205, 0.334666, 
            0.297272, 0.840118, 0.0237427, 0.168081), 
       nrow=20, 
       ncol=4,byrow=TRUE);
fm.fittingKinteractiveMC(d,env,2,0.6)
  

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

Description

Estimate values of the k-interacive fuzzy measures from empirical data using marginal representation.

Usage

fm.fittingKinteractiveMarginal(data, env=NULL, kadd="NA", K="NA", submod ="NA")

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
d <-  matrix( c( 0.00125122, 0.563568, 0.193298, 0.164338, 
            0.808716, 0.584991, 0.479858, 0.544309, 
            0.350281, 0.895935, 0.822815, 0.625868, 
            0.746582, 0.174103, 0.858917, 0.480347, 
            0.71048, 0.513519, 0.303986, 0.387631, 
            0.0149841, 0.0914001, 0.364441, 0.134229, 
            0.147308, 0.165894, 0.988495, 0.388044, 
            0.445679, 0.11908, 0.00466919, 0.0897714, 
            0.00891113, 0.377869, 0.531647, 0.258585, 
            0.571167, 0.601746, 0.607147, 0.589803, 
            0.166229, 0.663025, 0.450775, 0.357412, 
            0.352112, 0.0570374, 0.607666, 0.270228, 
            0.783295, 0.802582, 0.519867, 0.583348, 
            0.301941, 0.875946, 0.726654, 0.562174, 
            0.955872, 0.92569, 0.539337, 0.633631, 
            0.142334, 0.462067, 0.235321, 0.228419, 
            0.862213, 0.209595, 0.779633, 0.498077, 
            0.843628, 0.996765, 0.999664, 0.930197, 
            0.611481, 0.92426, 0.266205, 0.334666, 
            0.297272, 0.840118, 0.0237427, 0.168081), 
       nrow=20, 
       ncol=4,byrow=TRUE);
fm.fittingKinteractiveMarginal(d,env,2,0.6, 0)
  

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

Description

Estimate values of the k-interacive fuzzy measures from empirical data using marginal representation and maximal chains method.

Usage

fm.fittingKinteractiveMarginalMC(data, env=NULL, kadd="NA", K="NA", submod ="NA")

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
d <-  matrix( c( 0.00125122, 0.563568, 0.193298, 0.164338, 
            0.808716, 0.584991, 0.479858, 0.544309, 
            0.350281, 0.895935, 0.822815, 0.625868, 
            0.746582, 0.174103, 0.858917, 0.480347, 
            0.71048, 0.513519, 0.303986, 0.387631, 
            0.0149841, 0.0914001, 0.364441, 0.134229, 
            0.147308, 0.165894, 0.988495, 0.388044, 
            0.445679, 0.11908, 0.00466919, 0.0897714, 
            0.00891113, 0.377869, 0.531647, 0.258585, 
            0.571167, 0.601746, 0.607147, 0.589803, 
            0.166229, 0.663025, 0.450775, 0.357412, 
            0.352112, 0.0570374, 0.607666, 0.270228, 
            0.783295, 0.802582, 0.519867, 0.583348, 
            0.301941, 0.875946, 0.726654, 0.562174, 
            0.955872, 0.92569, 0.539337, 0.633631, 
            0.142334, 0.462067, 0.235321, 0.228419, 
            0.862213, 0.209595, 0.779633, 0.498077, 
            0.843628, 0.996765, 0.999664, 0.930197, 
            0.611481, 0.92426, 0.266205, 0.334666, 
            0.297272, 0.840118, 0.0237427, 0.168081), 
       nrow=20, 
       ncol=4,byrow=TRUE);
fm.fittingKinteractiveMarginalMC(d,env,2,0.6,0)
  

Fuzzy Measure Fitting function of the k-maxitive

Description

Estimate values of the k-maxitive fuzzy measures from empirical data.

Usage

fm.fittingKmaxitive(data, env=NULL, kadd="NA")

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
d <-  matrix( c( 0.00125122, 0.563568, 0.193298, 0.164338, 
            0.808716, 0.584991, 0.479858, 0.544309, 
            0.350281, 0.895935, 0.822815, 0.625868, 
            0.746582, 0.174103, 0.858917, 0.480347, 
            0.71048, 0.513519, 0.303986, 0.387631, 
            0.0149841, 0.0914001, 0.364441, 0.134229, 
            0.147308, 0.165894, 0.988495, 0.388044, 
            0.445679, 0.11908, 0.00466919, 0.0897714, 
            0.00891113, 0.377869, 0.531647, 0.258585, 
            0.571167, 0.601746, 0.607147, 0.589803, 
            0.166229, 0.663025, 0.450775, 0.357412, 
            0.352112, 0.0570374, 0.607666, 0.270228, 
            0.783295, 0.802582, 0.519867, 0.583348, 
            0.301941, 0.875946, 0.726654, 0.562174, 
            0.955872, 0.92569, 0.539337, 0.633631, 
            0.142334, 0.462067, 0.235321, 0.228419, 
            0.862213, 0.209595, 0.779633, 0.498077, 
            0.843628, 0.996765, 0.999664, 0.930197, 
            0.611481, 0.92426, 0.266205, 0.334666, 
            0.297272, 0.840118, 0.0237427, 0.168081), 
       nrow=20, 
       ncol=4,byrow=TRUE);
fm.fittingKmaxitive(d,env,2)
  

Fuzzy Measure Fitting function of the k-tolerant

Description

Estimate values of the k-tolerant fuzzy measures from empirical data.

Usage

fm.fittingKtolerant(data, env=NULL, kadd="NA")

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
d <-  matrix( c( 0.00125122, 0.563568, 0.193298, 0.164338, 
            0.808716, 0.584991, 0.479858, 0.544309, 
            0.350281, 0.895935, 0.822815, 0.625868, 
            0.746582, 0.174103, 0.858917, 0.480347, 
            0.71048, 0.513519, 0.303986, 0.387631, 
            0.0149841, 0.0914001, 0.364441, 0.134229, 
            0.147308, 0.165894, 0.988495, 0.388044, 
            0.445679, 0.11908, 0.00466919, 0.0897714, 
            0.00891113, 0.377869, 0.531647, 0.258585, 
            0.571167, 0.601746, 0.607147, 0.589803, 
            0.166229, 0.663025, 0.450775, 0.357412, 
            0.352112, 0.0570374, 0.607666, 0.270228, 
            0.783295, 0.802582, 0.519867, 0.583348, 
            0.301941, 0.875946, 0.726654, 0.562174, 
            0.955872, 0.92569, 0.539337, 0.633631, 
            0.142334, 0.462067, 0.235321, 0.228419, 
            0.862213, 0.209595, 0.779633, 0.498077, 
            0.843628, 0.996765, 0.999664, 0.930197, 
            0.611481, 0.92426, 0.266205, 0.334666, 
            0.297272, 0.840118, 0.0237427, 0.168081), 
       nrow=20, 
       ncol=4,byrow=TRUE);
fm.fittingKtolerant(d,env,2)
  

Mobius Fuzzy Measure Fitting function

Description

Estimate values of the Mobius fuzzy measures from empirical data.

Usage

fm.fittingMob(data, env=NULL ,kadd="NA")

Arguments

Value

Note

The fit might not be perfect, and not all the constraints can be fully met.

Author(s)

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

Examples

d <-  matrix( c( 0.00125122, 0.563568, 0.193298, 0.164338, 
            0.808716, 0.584991, 0.479858, 0.544309, 
            0.350281, 0.895935, 0.822815, 0.625868, 
            0.746582, 0.174103, 0.858917, 0.480347, 
            0.71048, 0.513519, 0.303986, 0.387631, 
            0.0149841, 0.0914001, 0.364441, 0.134229, 
            0.147308, 0.165894, 0.988495, 0.388044, 
            0.445679, 0.11908, 0.00466919, 0.0897714, 
            0.00891113, 0.377869, 0.531647, 0.258585, 
            0.571167, 0.601746, 0.607147, 0.589803, 
            0.166229, 0.663025, 0.450775, 0.357412, 
            0.352112, 0.0570374, 0.607666, 0.270228, 
            0.783295, 0.802582, 0.519867, 0.583348, 
            0.301941, 0.875946, 0.726654, 0.562174, 
            0.955872, 0.92569, 0.539337, 0.633631, 
            0.142334, 0.462067, 0.235321, 0.228419, 
            0.862213, 0.209595, 0.779633, 0.498077, 
            0.843628, 0.996765, 0.999664, 0.930197, 
            0.611481, 0.92426, 0.266205, 0.334666, 
            0.297272, 0.840118, 0.0237427, 0.168081), 
       nrow=20, 
       ncol=4,byrow=TRUE);
env<-fm.Init(3)
fm.fittingMob(d,env)
  

Symmetric Fuzzy Measure Fitting function

Description

Estimate values of the symmetric fuzzy measures from empirical data. The resulting Choquet integral is the OWA function.

Usage

fm.fittingOWA(data, env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
d <-  matrix( c( 0.00125122, 0.563568, 0.193298, 0.164338, 
            0.808716, 0.584991, 0.479858, 0.544309, 
            0.350281, 0.895935, 0.822815, 0.625868, 
            0.746582, 0.174103, 0.858917, 0.480347, 
            0.71048, 0.513519, 0.303986, 0.387631, 
            0.0149841, 0.0914001, 0.364441, 0.134229, 
            0.147308, 0.165894, 0.988495, 0.388044, 
            0.445679, 0.11908, 0.00466919, 0.0897714, 
            0.00891113, 0.377869, 0.531647, 0.258585, 
            0.571167, 0.601746, 0.607147, 0.589803, 
            0.166229, 0.663025, 0.450775, 0.357412, 
            0.352112, 0.0570374, 0.607666, 0.270228, 
            0.783295, 0.802582, 0.519867, 0.583348, 
            0.301941, 0.875946, 0.726654, 0.562174, 
            0.955872, 0.92569, 0.539337, 0.633631, 
            0.142334, 0.462067, 0.235321, 0.228419, 
            0.862213, 0.209595, 0.779633, 0.498077, 
            0.843628, 0.996765, 0.999664, 0.930197, 
            0.611481, 0.92426, 0.266205, 0.334666, 
            0.297272, 0.840118, 0.0237427, 0.168081), 
       nrow=20, 
       ncol=4,byrow=TRUE);
fm.fittingOWA(d,env)
  

Additive Fuzzy Measure Fitting function

Description

Estimate values of an additive fuzzy measure from empirical data. In this case the Choquet integral is the weighted arithmetic mean WAM.

Usage

fm.fittingWAM(data, env=NULL)

Arguments

Value

Author(s)

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

Examples

env<-fm.Init(3)
d <-  matrix( c( 0.00125122, 0.563568, 0.193298, 0.164338, 
            0.808716, 0.584991, 0.479858, 0.544309, 
            0.350281, 0.895935, 0.822815, 0.625868, 
            0.746582, 0.174103, 0.858917, 0.480347, 
            0.71048, 0.513519, 0.303986, 0.387631, 
            0.0149841, 0.0914001, 0.364441, 0.134229, 
            0.147308, 0.165894, 0.988495, 0.388044, 
            0.445679, 0.11908, 0.00466919, 0.0897714, 
            0.00891113, 0.377869, 0.531647, 0.258585, 
            0.571167, 0.601746, 0.607147, 0.589803, 
            0.166229, 0.663025, 0.450775, 0.357412, 
            0.352112, 0.0570374, 0.607666, 0.270228, 
            0.783295, 0.802582, 0.519867, 0.583348, 
            0.301941, 0.875946, 0.726654, 0.562174, 
            0.955872, 0.92569, 0.539337, 0.633631, 
            0.142334, 0.462067, 0.235321, 0.228419, 
            0.862213, 0.209595, 0.779633, 0.498077, 
            0.843628, 0.996765, 0.999664, 0.930197, 
            0.611481, 0.92426, 0.266205, 0.334666, 
            0.297272, 0.840118, 0.0237427, 0.168081), 
       nrow=20, 
       ncol=4,byrow=TRUE);
fm.fittingWAM(d,env)
  

Function for returning the length of the array

Description

Returns the length of the array of values of k-interactive fuzzy measures. Useful for reserving memory.

Usage

  fm.fm_arraysize(env = NULL, kint = "NA")

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(3)
  arraylength <- fm.fm_arraysize(env,1)
  

Function for generating one antibuoyant random fuzzy measure

Description

Generates one antibuoyant random fuzzy measure in standard representation.

Usage

  fm.generate_antibuoyant(env = NULL)

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(3)
  fuzzymeasures <- fm.generate_antibuoyant(env)
  fuzzymeasures 

Function for random generation of balanced fuzzy measures in standard representation

Description

Generate several balanced random fuzzy measures in standard representation.

Usage

  fm.generate_balanced(num, env=NULL)

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(3)
  fuzzymeasures  <- fm.generate_balanced(2, env)
  fuzzymeasures
  

Function for random generation of belief fuzzy measures in standard representation

Description

Generate several random k-additive belief measures in Mobius representation.

Usage

  fm.generate_belief(num, kadd, env=NULL)

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(5)
  belief  <- fm.generate_belief(2, 3, env)
  # 2 3-additive measures with n=5
  belief
  

Function for generating 2-additive fuzzy measures in Mobius representation

Description

Generates num random 2-additive fuzzy measures in Mobius representation.

Usage

  fm.generate_fm_2additive(num, n)

Arguments

Value

Author(s)

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

Examples

    

num <- 2
n <- 5
fuzzymeasures <- fm.generate_fm_2additive(num,n)
fuzzymeasures$V
fuzzymeasures$len

  

Function for generating 2additive concave fuzzy measures.

Description

Generates num 2-additive concave (supermodular) fuzzy measures for n inputs.

Usage

  fm.generate_fm_2additive_concave(num, n)

Arguments

Value

Author(s)

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

Examples

  fuzzymeasures <- fm.generate_fm_2additive_concave(10,20)
  

Function for generating 2-additive convex fuzzy measures

Description

Generates num 2-additive convex (supermodular) fuzzy measures for n inputs.

Usage

  fm.generate_fm_2additive_convex(num, n)

Arguments

Value

Author(s)

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

Examples

  addconvex <- fm.generate_fm_2additive_convex(5,20)

  

Function for generating 2additive convex numbers in sparse representation

Description

Generates a random 2-additive supermodular fuzzy measure in sparse representation.

Usage

  fm.generate_fm_2additive_convex_sparse(n, envsp = NULL)

Arguments

Value

Author(s)

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

Examples

  n <- 5
  tups<-vector()
  tupsidx<-vector()
  envsp <- fm.PrepareSparseFM(n, tups,tupsidx) 
  envsp <- fm.generate_fm_2additive_convex_sparse(n, envsp)
  envsp
     envsp <- fm.FreeSparseFM(envsp) 
  

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

Description

Generates num 2-additive convex (supermodular) fuzzy measures for n inputs. Some of the interaction indices are set to 0 (independence).

Usage

  fm.generate_fm_2additive_convex_withsomeindependent(num, n)

Arguments

Value

Author(s)

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

Examples

  addconvex <- fm.generate_fm_2additive_convex_withsomeindependent(5,20)

  

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

Description

Generate a random 2-additive fuzzy measures in Mobius representation by using random walk.

Usage

  fm.generate_fm_2additive_randomwalk2(num, n, markov, option, step, Fn)

Arguments

Value

Author(s)

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

Examples

 
  num <- 10
  n <- 5
  fuzzymeasures <- fm.generate_fm_2additive_randomwalk2(num, n, 1000, 0, 0.001, NULL)

Generate kadditive convex sparse fuzzy measures

Description

Generates a random k-additive Belief fuzzy measure in sparse representation

Usage

  fm.generate_fm_kadditive_convex_sparse(n, kadd, nonzero, envsp = NULL)

Arguments

Value

Author(s)

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

Examples

    n <- 5
  tups<-vector()
  tupsidx<-vector()
  envsp <- fm.PrepareSparseFM(n, tups,tupsidx) 
  envsp <- fm.generate_fm_kadditive_convex_sparse(n,4,10, envsp)
  envsp
     envsp <- fm.FreeSparseFM(envsp) 
  

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

Description

Generates num k-interactive dual concave fuzzy measures in Mobius representation using random walk of length markov of stepsize step

Usage

  fm.generate_fm_kinteractivedualconcave(num, n, kadd, markov,  step,  Fn, env)

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(4)
  step <- 0.001
  Fn <- NULL

  fuzzymeasures <- fm.generate_fm_kinteractivedualconcave(10, 4, 2, 1000, step, Fn, env)
  fuzzymeasures 

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

Description

Generates num k-interactive dual convex fuzzy measures in Mobius representation using random walk of length markov of stepsize step.

Usage

  fm.generate_fm_kinteractivedualconvex(num, n, kadd, markov,  step, Fn, env)

Arguments

Value

Author(s)

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(10, 4, 2, 1000, step, Fn, env)
  fuzzymeasures 
  
  env<-fm.Free(env)

Generate randomly fuzzy measures

Description

Generate several random fuzzy measures (num is their number) stored in cardinality ordering in the array v using minimals_plus method.

Usage

  fm.generate_fm_minplus(num, kint, markov, option, K, env = NULL)

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(3)
  fuzzymeasures <- fm.generate_fm_minplus(10,3,1000,0,0.7, env)
  fuzzymeasures 

Function for generating several k-additive fuzzy measure

Description

Generates num k-additive fuzzy measures in the standard or Mobius representation using random walk of length markov of stepsize step.

Usage

  fm.generate_fm_randomwalk(num, n, kadd, markov, option, step, Fn, env)

Arguments

Value

Author(s)

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

Examples

 
   Fn <- function(n,v){
        out <- 0.0

        for(i in 1:n) out<- out+v[i];
        
        if(out>1) {
        return(0)
        } else
        return(1)
    }
    env<-fm.Init(3)
    step <- 0.0010
    Option <- 3
    n <- 3

  fuzzymeasures <- fm.generate_fm_randomwalk(2, 3, 2, 1000, Option, step, Fn, env)
  print(fuzzymeasures)
  print(fuzzymeasures$length)

Function for random generation of fuzzy measures in standard representation

Description

Generate several random fuzzy measures in standard representation

Usage

  fm.generate_fm_sorting(num, markov, option, env = NULL)

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(3)
  markovsteps <- 100
  fuzzymeasures <- fm.generate_fm_sorting(5, markovsteps, 0, env)
  fuzzymeasures

Function for random generation of fuzzy measures

Description

Generate several random fuzzy measures (num is their number) stored in cardinality ordering in the array v using topological sort.

Usage

  fm.generate_fm_tsort(num, kint, markov, option, K, env = NULL)

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(3)
  fuzzymeasures <- fm.generate_fm_tsort(10,3,1000,0,0.7, env)
  fuzzymeasures
  

Function for generating convex fuzzy measures

Description

Generates num convex random fuzzy measures stored consecutively in cardinality ordering in the output array.

Usage

  fm.generate_fmconvex_tsort(num, kint, markov, option, K, env = NULL)

Arguments

Value

Author(s)

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

Examples

 
  env<-fm.Init(3)
  fuzzymeasures <- fm.generate_fmconvex_tsort(1,3,1000,0,1, env)
  

Function for exporting number of tuples

Description

Returns the number of tuples.

Usage

  fm.get_num_tuples(envsp=NULL)

Arguments

Value

Author(s)

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

Examples

  n <- 3
  envsp <- fm.PrepareSparseFM(n, vector(), vector()) 
  envsp <- fm.add_singletons_sparse(c(0.2,0.1,0.2),envsp) 
  envsp <- fm.add_tuple_sparse(c(1,2,3),0.4,envsp);
  fm.get_num_tuples(envsp)

  envsp <-fm.FreeSparseFM(envsp)  

Function for exporting the size of the array of tuples

Description

Returns the length of the array of tuples.

Usage

  fm.get_sizearray_tuples(envsp=NULL)

Arguments

Value

Author(s)

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

Examples

  n <- 3
  envsp <- fm.PrepareSparseFM(n, vector(), vector()) 
  envsp <- fm.add_singletons_sparse(c(0.2,0.1,0.2),envsp) 
  envsp <- fm.add_tuple_sparse(c(1,2,3),0.4,envsp);
  fm.get_sizearray_tuples(envsp)

  envsp <- fm.FreeSparseFM(envsp)

Function for checking if i belongs to the tuple A

Description

Checks if element i (1-based) belongs to the tuple indexed A (whose cardinality can be 1,2, other (automatically determined)).

Usage

  fm.is_inset_sparse(A, card, i, envsp=NULL)

Arguments

Value

Author(s)

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

Examples

  n <- 3
  envsp <- fm.PrepareSparseFM(n, vector(), vector()) 
  envsp <- fm.add_singletons_sparse(c(0.2,0.1,0.2),envsp) 
  envsp <- fm.add_tuple_sparse(c(1,2,3),0.4,envsp);

  fm.is_inset_sparse(0,3,1,envsp)
  fm.is_inset_sparse(0,3,4,envsp)

  envsp <- fm.FreeSparseFM(envsp)

Function for checking if tuple B is subset of tuple A

Description

Checks if tuple B is a subset of tuple A, The cardinalities of both tuples need to be supplied.

Usage

  fm.is_subset_sparse(A, cardA, B, cardB, envsp = NULL)

Arguments

Value

Author(s)

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

Examples

  n <- 3
  envsp <- fm.PrepareSparseFM(n, vector(), vector()) 
  envsp <- fm.add_singletons_sparse(c(0.2,0.1,0.2),envsp) 
  envsp <- fm.add_tuple_sparse(c(1,2,3),0.4,envsp);
  envsp <- fm.add_pair_sparse(1,2,0.2,envsp);
  envsp <- fm.add_pair_sparse(1,3,0.3,envsp);

  fm.is_subset_sparse(0,3,0,2,envsp) #is 0th pair a subset of the 0th tuple?
  fm.is_subset_sparse(0,3,1,2,envsp) #is 1th pair a subset of the 0th tuple?

  envsp<-fm.FreeSparseFM(envsp)	

Maximun of x computation function in sparse representation

Description

Calculates maximum of x with the indices belonging to tuple indexed as S

Usage

  fm.max_subset_sparse(x, S, cardS, envsp=NULL)

Arguments

Value

Author(s)

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

Examples

  n <- 3
  envsp <- fm.PrepareSparseFM(n, vector(), vector()) 
  envsp <- fm.add_singletons_sparse(c(0.2,0.1,0.2),envsp) 
  envsp <- fm.add_tuple_sparse(c(1,2,3),0.4,envsp);

  fm.max_subset_sparse(c(0.1,0.05,0.2),0,3,envsp)
  envsp <- fm.FreeSparseFM(envsp) 

Minimun of x computation function in sparse representation

Description

Calculates minimum of x with the indices belonging to tuple indexed as S

Usage

  fm.min_subset_sparse(x, S, cardS, envsp=NULL)

Arguments

Value

Author(s)

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

Examples

  n <- 3
  envsp <- fm.PrepareSparseFM(n, vector(), vector()) 
  envsp <- fm.add_singletons_sparse(c(0.2,0.1,0.2),envsp) 
  envsp <- fm.add_tuple_sparse(c(1,2,3),0.4,envsp);

  fm.min_subset_sparse(c(0.1,0.05,0.2),0,3,envsp)
   envsp <- fm.FreeSparseFM(envsp) 

Function for populating 2-additive sparse capacity

Description

Populate 2-additive sparse capacity with nonzero values using the singletons and two arrays of indices (of size numpairs).

Usage

  fm.populate_fm_2add_sparse(singletons, numpairs, pairs, indicesp1, indicesp2, envsp)

Arguments

Value

Author(s)

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

Examples

    n <- 3
    envsp <- fm.PrepareSparseFM(n, vector(), vector()) 

   envsp <- fm.populate_fm_2add_sparse(c(0.1,0.2,0.3), 3, 
              c(0.4,0.5,0.6), c(1,1,2), c(2,3,3), envsp)
    envsp
    envsp <- fm.FreeSparseFM(envsp) 
  

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

Description

Given 2-additive capacity singletons+pairs in one array v , selects nonzero pairs and populates sparse capacity envsp

Usage

  fm.populate_fm_2add_sparse_from2add(n, v, envsp=NULL)

Arguments

Value

Author(s)

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

Examples

      n <- 3
      envsp <- fm.PrepareSparseFM(n, vector(), vector()) 
      envsp <- fm.populate_fm_2add_sparse_from2add(3,c(0.4,0.5,0.6, 0, 0, 0.1),envsp)
envsp
     envsp <- fm.FreeSparseFM(envsp) 	
  

Get pairs computation function in sparse representation

Description

Export the internal arrays of the sparse capacity as arrays of singletons, pairs and tuples.

Usage

  fm.sparse_get_pairs( envsp=NULL)

Arguments

Value

Author(s)

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

Examples

    n <- 3
    envsp <- fm.PrepareSparseFM(n)
    envsp <-fm.add_pair_sparse(1,2, 0.4, envsp)
    envsp <-fm.add_pair_sparse(1,3, 0.3, envsp)

    pairs <- fm.sparse_get_pairs(envsp)
    pairs
         envsp <- fm.FreeSparseFM(envsp) 
  

Get singletons of sparse fuzzy measure

Description

Export the internal arrays of the sparse capacity as arrays of singletons, pairs and tuples.

Usage

  fm.sparse_get_singletons(envsp=NULL)

Arguments

Value

Author(s)

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

Examples

  n <- 3
  envsp <- fm.PrepareSparseFM(n)
  envsp <- fm.add_singletons_sparse(c(0, 0.3, 0.5),envsp)
  singletons <- fm.sparse_get_singletons(envsp)
  singletons
       envsp <- fm.FreeSparseFM(envsp) 

Get tuples of a sparse fuzzy measure

Description

Export the internal arrays of the sparse capacity as arrays of singletons, pairs and tuples.

Usage

  fm.sparse_get_tuples(envsp=NULL)

Arguments

Value

Author(s)

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

Examples

    n <- 3
    envsp <- fm.PrepareSparseFM(n) 
    envsp <- fm.add_tuple_sparse(c(1,2,3),0.2,envsp)
    envsp <- fm.add_tuple_sparse(c(1,3,4),0.3,envsp)

    tuples <- fm.sparse_get_tuples(envsp)
    tuples
     envsp <- fm.FreeSparseFM(envsp) 
    
  

Test function

Description

This function provide some examples of how fuzzy measure operation in this toolbox are used. It can be used to test if the toolbox has been installed successfully or not.

Usage

fm.test()

Author(s)

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

Examples

fm.test()

Tuple cardinality

Description

Returns the cardinality of the tuple numbered i in the list of tuples.

Usage

  fm.tuple_cardinality_sparse(i, envsp = NULL)

Arguments

Value

Author(s)

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

Examples

    n <- 3
    envsp <- fm.PrepareSparseFM(n, c(0.2,0.4,0.1), c(2,1,2,2,1,3,3,1,2,3)) 
    fm.tuple_cardinality_sparse(0,envsp)
     envsp <- fm.FreeSparseFM(envsp)