fm.fittingWAM {Rfmtool}

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

data

Empirical data set in pairs (x_1,y_1),(x_2,y_2),...,(x_d,y_d) where x_i in [0,1]^n is a vector containing utility values of n input criteria x_i1,x_i2,...,x_in,y_i in [0,1] is a single aggregated value given by decision makers. The data is stored as a matrix of M by n+1 elements, where M is the number of data instances, and n is the number of input criteria, the column n + 1 stores the observed aggregated value y.

env

Environment variable obtained from fm.Init(n).

Value

output

The output is an array of size n containing estimated weighting vector of WAM.

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)