# fm.fittingKmaxitive: Fuzzy Measure Fitting function In Rfmtool: Fuzzy Measure Tools

## Description

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

## Usage

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

## Arguments

 `data` is the 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). `kadd` is the value of k-maxitivity, which is used for reducing the complexity of fuzzy measures. kadd is defined as an optional argument, its default value is kadd = n.

## Value

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

## Author(s)

Gleb Beliakov, Andrei Kelarev, Quan Vu, Deakin University

## References

[1] http://www.deakin.edu.au/~gleb/fmtools.html [2] H.Q. Vu, G. Beliakov, G. Li, 2014, A choquet integral toolbox and its application in customer preference analysis, in Data mining applications with R, Elsevier Inc., Waltham, MA., pp.247-272.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ```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); fm.fittingKmaxitive(d,env,2) ```

Rfmtool documentation built on June 5, 2018, 5:04 p.m.