CPP.Gini: CPP by the Gini Index, using Beta PERT distributions

In CPP: Composition of Probabilistic Preferences (CPP)

Description

The CPP by the Gini Index is used to rank alternatives by evenness of evaluations, in multicriteria decision problems.

Usage

CPP.Gini(x, s)

Arguments

x	Decision matrix of Alternatives (rows) and Criteria (columns). Benefit criteria must be positive and cost criteria must be negative.
s	Shape of Beta PERT distribution, as described in the package 'mc2d'. There is no default value, however the higher the shape the higher the kurtosis.

Value

PMax are the joint probabilities of each alternative being higher than the others, per criterion. CPP.Gini returns the alternatives' scores by the Gini Index and their respective preference ranks for decisionmaking.

References

Sant'Anna, Annibal P. (2015). Probabilistic Composition of Preferences: Theory and Applications, Springer

Gaviao, Luiz O. & Lima, Gilson B.A. (2017) Support decision to player selection: an application of the CPP in soccer, Novas Edições Acadêmicas [in Portuguese].

Examples

# Alternatives' original scores
Alt.1 = c(2,30,86,-5)
Alt.2 = c(4,26,77,-12)
Alt.3 = c(3,22,93,-4)
Alt.4 = c(6,34,65,-10)
Alt.5 = c(5,31,80,-8)
x = rbind(Alt.1,Alt.2,Alt.3,Alt.4,Alt.5) # Decision matrix
s = 4 # Shape
CPP.Gini(x,s)

Example output

Loading required package: ineq
Loading required package: kappalab
Loading required package: lpSolve
Loading required package: quadprog
Loading required package: kernlab

Attaching package: ‘kappalab’

The following object is masked from ‘package:ineq’:

    entropy

Loading required package: mc2d
Loading required package: mvtnorm

Attaching package: ‘mc2d’

The following objects are masked from ‘package:base’:

    pmax, pmin

$PMax
              [,1]         [,2]         [,3]        [,4]
Alt.1 0.0007955106 0.1125811655 0.1932253309 0.321516022
Alt.2 0.0481882455 0.0127144775 0.0280102853 0.000498611
Alt.3 0.0084272819 0.0005753932 0.7221231766 0.636892590
Alt.4 0.7403114127 0.6934705803 0.0006767439 0.005717123
Alt.5 0.2022775493 0.1806583757 0.0559644616 0.035375673

$CPP.Gini
         Index Rank
[1,] 0.4150517    2
[2,] 0.4427968    3
[3,] 0.5104296    5
[4,] 0.5045664    4
[5,] 0.3296601    1

CPP documentation built on May 2, 2019, 1:34 p.m.