OutrankingTools (version 1.0)

Electre3_AlphaBetaThresholds: ELECTRE III using affine function form of the thresholds

Description

ELECTRE III method aims to answer the following question: considering a finite set of actions, A, evaluated on a coherent family of pseudo-criteria, F, how to make a partition of A in classes of quivalence and provide a necessarily complete pre-order expressing the relative position of these classes? In the first phase, ELECTRE III method involves the construction of a fuzzy outranking relation. In the second phase, an algorithm is used for making a ranking in a final partial pre-order, that combines two complete pre-orders.

Usage

Electre3_AlphaBetaThresholds(performanceMatrix,
alternatives,
criteria,
minmaxcriteria,
criteriaWeights,
alpha_q,
beta_q,
alpha_p,
beta_p,
alpha_v,
beta_v,
mode_def)

Arguments

performanceMatrix

Matrix or data frame containing the performance table. Each row corresponds to an alternative, and each column to a criterion. Rows (resp. columns) must be named according to the IDs of the alternatives (resp. criteria).

alternatives

Vector containing names of alternatives, according to which the data should be filtered.

criteria

Vector containing names of criteria, according to which the data should be filtered.

minmaxcriteria

criteriaMinMax Vector containing the preference direction on each of the criteria. "min" (resp."max") indicates that the criterion has to be minimized (maximized).

criteriaWeights

Vector containing the weights of the criteria.

alpha_q

Vector containing the coefficients alpha when indifference threshold is as affine function of the performance.

beta_q

Vector containing coefficients beta when indifference threshold is as affine function of the performance.

alpha_p

Vector containing coefficients beta when preference threshold is as affine function of the performance.

beta_p

Vector containing coefficients beta when preference threshold is as affine function of the performance.

alpha_v

Vector containing coefficients beta when veto threshold is as affine function of the performance.

beta_v

Vector containing coefficients beta when veto threshold is as affine function of the performance.

mode_def

Vector containing the mode of definition which indicates the mode of calculation of the thresholds (direct (D), considers the worst of the two actions; inverse(I), considers the best of the two actions). If Null, "Direct" mode will be setting

References

Roy B. : "The outranking approach and the foundations of ELECTRE methods", Theory and Decision 31, 1991, 49-73.

Examples

## Illustrative example used  to present the ELECTRE III-IV software in the French version. 
## The objective: make the ranking of 10 French cars that were evaluated on 7 criteria
##(VALLE E, D. AND ZIELNIEWICZ, P. (1994a). 
## Document du LAMSADE 85, Universite Paris-Dauphine,Paris.)

## the performance table

performanceMatrix <- cbind(
c(103000,101300,156400,267400,49900,103600,103000,170100,279700,405000),
c(171.3,205.3,221.7,230.7,122.6,205.1,178.0,226.0,233.8,265.0),
c(7.65,7.90,7.90,10.50,8.30,8.20,7.20,9.10,10.90,10.30),
c(352,203,391,419,120,265,419,419,359,265),
c(11.6,8.4,8.4,8.6,23.7,8.1,11.4,8.1,7.8,6.0), 	
c(88.0,78.3,81.5,64.7,74.1,81.7,77.6,74.7,75.5,74.7),
c(69.7,73.4,69.0,65.6,76.4,73.6,66.2,71.7,70.9,72.0))

# Vector containing names of alternatives

alternatives<-c("CBX16","P205G","P405M","P605S","R4GTL","RCLIO","R21TS","R21TU","R25BA","ALPIN")

# Vector containing names of criteria

criteria <-c("Prix","Vmax","C120","Coff","Acce","Frei","Brui")
#  vector indicating the direction of the criteria evaluation .
minmaxcriteria <-c("min","max","min","max","min","min","min")

# criteriaWeights vector
criteriaWeights <- c(0.3,0.1,0.3,0.2,0.1,0.2,0.1)

# thresholds vector
alpha_q <- c(0.08,0.02,0,0,0.1,0,0)
beta_q <- c(-2000,0,1,100,-0.5,0,3)
alpha_p <- c(0.13,0.05,0,0,0.2,0,0)
beta_p <- c(-3000,0,2,200,-1,5,5)
alpha_v <- c(0.9,NA,0,NA,0.5,0,0)
beta_v <- c(50000,NA,4,NA,3,15,15)

# Vector containing the mode of definition which 
# indicates the mode of calculation of the thresholds.
mode_def <- c("I","D","D","D","D","D","D")

# Testing

Electre3_AlphaBetaThresholds(performanceMatrix,
								alternatives,
								criteria,
								minmaxcriteria,
								criteriaWeights,
								alpha_q,
								beta_q,
								alpha_p,
								beta_p,
								alpha_v,
								beta_v,
								mode_def)