The MAUT decision models are defined with aid of utility functionsu1, …, un which areevaluated over indexesx1, …, xn and thoseutilities are aggregated considering additional weightsw1, …, wn, the wholefinal utility is given by the sum
u(x1, …, xn)=∑1 ≤ i ≤ n wi ui (xi)
Withmau you can build and test decision modelsbased in Multi Attribute Utility Theory (MAUT). The utilities of anylevel of the decision model can be easily evaluated.
To installmau you can proceed in the following waymaking use of the devtools library
library( devtools )install_github("pedroguarderas/mau" )The utility functions for a MAUT model could be defined in apractical format when those are are piecewise defined like constant riskaverse functions, in such case it is only necessary to define theparameters of the function for each part of the domain of definition.This is because, the constant risk averse functions are of the formu(x)=a ⋅ x + b oru(x)=a ⋅ eb ⋅ x + c.
File format for the piecewise defintion of utilities, is specified asfollows. > Header
>
> Function name
> min1 max1 a1 b1 c1
> min2 max2 a2 b2 c2
> min3 max3 a3 b3 c3
> …
> Function name
> min1 max1 a1 b1 c1
> min2 max2 a2 b2 c2
> min3 max3 a3 b3 c3
> …
Ifci is 0 then the utility is linear,otherwise is an exponential function. For example:
library( mau )file<-system.file("extdata","utilities.txt",package ="mau" )lines<-readLines( file )for ( iin1:length( lines ) ) {cat( lines[i],'\n' )}#> Utilities#>#> Project#> 1 2 1.5 -0.5 0#> 2 3 1.5 -0.5 0#>#> Self implementation#> 1 2 1.5 -0.5 0#> 2 3 1.5 -0.5 0#>#> External and local relations#> 1 10 1 0 0#> 0 1 0 1 0#>#> Scope of capabilities#> 6 15 1 0 0#> 0 6 1.225 -1.225 0.2824In the sources below is developed a complete example of a decisionmodel, the packagemau is employed to load utilitiesdefined in the fileutilities.txt, provided in the packageitself, automatically the script with utilies is built and saved in thelocal working directory, after that withEval.Utilitiesevery function is evaluated over the columns of the index table, thenames for utilities were previously standarized withStand.String. With another filetree.csv thedecision tree associated to the MAUT model is built and every weight andrelative weight assigned with theMake.Decision.Treefunction, in addition the whole model with utilies of every criteria isobtained withCompute.Model. The simulation of constrainedweights is made withSim.Const.Weights, the result could beemployed for a sensitivy test of the decision model under a variation ofweights.
# Loading packages --------------------------------------------------------------------------------library( mau )library( data.table )library( igraph )library( ggplot2 )# Table of indexes --------------------------------------------------------------------------------index<-data.table(cod =paste('A',1:10,sep ='' ),i1 =c(0.34,1,1,1,1,0.2,0.7,0.5,0.11,0.8 ),i2 =c(0.5,0.5,1,0.5,0.3,0.1,0.4,0.13,1,0.74 ),i3 =c(0.5,1.0,0.75,0.25,0.1,0.38,0.57,0.97,0.3,0.76 ),i4 =c(0,0.26,0.67,0.74,0.84,0.85,0.74,0.65,0.37,0.92 ) )# Loading utilities -------------------------------------------------------------------------------file<-system.file("extdata","utilities.txt",package ="mau" )script<-'utilities.R'lines<-17skip<-2encoding<-'utf-8'functions<-Read.Utilities( file, script, lines, skip, encoding )source('utilities.R' )# Index positions ---------------------------------------------------------------------------------columns<-c(2,3,4,5 )# Function namesfunctions<-sapply(c('Project','Self implementation','External and local relations','Scope of capabilities' ),FUN = Stand.String )names( functions )<-NULL# Evaluation of utilities -------------------------------------------------------------------------utilities<-Eval.Utilities( index, columns, functions )# Tree creation -----------------------------------------------------------------------------------file<-system.file("extdata","tree.csv",package ="mau" )tree.data<-Read.Tree( file,skip =0,nrow =8 )tree<-Make.Decision.Tree( tree.data )# Compute the decision model ----------------------------------------------------------------------weights<-tree.data[!is.na( weight ) ]$weightmodel<-Compute.Model( tree, utilities, weights )# Weights simulation ------------------------------------------------------------------------------n<-200alpha<-c(0.2,0.5,0.1,0.2 )constraints<-list(list(c(1,2),0.7 ),list(c(3,4),0.3 ) )S<-Sim.Const.Weights( n, utilities, alpha, constraints )plot.S<-Plot.Simulation.Weight( S$simulation,title ='Simulations',xlab ='ID',ylab ='Utility' )plot( plot.S )