fm.fittingMob: Mobius Fuzzy Measure Fitting function

In Rfmtool: Fuzzy Measure Tools

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

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 store the observed aggregating value y.
env	Environment variable obtained from fm.Init(n).
kadd	value of k-additivity, which is used for reducing the complexity of fuzzy measures. kadd is defined as an optional argument, its defaultvalue is kadd = n.

Value

output

The output is an array of size 2^n containing estimated Mobius fuzzy measure in binary ordering.

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);
env<-fm.Init(3)
fm.fittingMob(d,env)
  

Rfmtool documentation built on Feb. 16, 2023, 9:21 p.m.