additiveValueFunctionElicitation {MCDA}

Elicitation of a general additive value function.

Description

Elicits a general additive value function from a ranking of alternatives.

Usage

additiveValueFunctionElicitation(
  performanceTable,
  criteriaMinMax,
  epsilon,
  alternativesRanks = NULL,
  alternativesPreferences = NULL,
  alternativesIndifferences = NULL,
  alternativesIDs = NULL,
  criteriaIDs = NULL
)

Arguments

performanceTable

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).

criteriaMinMax

Vector containing the preference direction on each of the criteria. "min" (resp. "max") indicates that the criterion has to be minimized (maximized). The elements are named according to the IDs of the criteria.

epsilon

Numeric value containing the minimal difference in value between two consecutive alternatives in the final ranking.

alternativesRanks

Optional vector containing the ranks of the alternatives. The elements are named according to the IDs of the alternatives. If not present, then at least one of alternativesPreferences or alternativesIndifferences should be given.

alternativesPreferences

Optional matrix containing the preference constraints on the alternatives. Each line of the matrix corresponds to a constraint of the type alternative a is strictly preferred to alternative b. If not present, then either alternativesRanks or alternativesIndifferences should be given.

alternativesIndifferences

Optional matrix containing the indifference constraints on the alternatives. Each line of the matrix corresponds to a constraint of the type alternative a is indifferent to alternative b. If not present, then either alternativesRanks or alternativesPreferences should be given.

alternativesIDs

Vector containing IDs of alternatives, according to which the datashould be filtered.

criteriaIDs

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

Value

The function returns a list structured as follows :

optimum

The value of the objective function.

valueFunctions

A list containing the value functions which have been determined. Each value function is defined by a matrix of breakpoints, where the first row corresponds to the abscissa (row labelled "x") and where the second row corresponds to the ordinate (row labelled "y").

overallValues

A vector containing the overall values of the input alternatives.

ranks

A vector containing the ranks of the alternatives obtained via the elicited value functions. Ties method = "min".

Kendall

Kendall's tau between the input ranking and the one obtained via the elicited value functions.

errors

The errors (sigma) which have to be added to the overall values of the alternatives in order to respect the input ranking.

References

Based on the UTA algorithm (E. Jacquet-Lagreze, J. Siskos, Assessing a set of additive utility functions for multicriteria decision-making, the UTA method, European Journal of Operational Research, Volume 10, Issue 2, 151–164, June 1982) except that the breakpoints of the value functions are the actual performances of the alternatives on the criteria.

Examples

# ----------------------------------------
# ranking some cars (from original article on UTA by Siskos and Lagreze, 1982)

# the separation threshold

epsilon <-0.01

# the performance table

performanceTable <- rbind(      
c(173, 11.4, 10.01, 10, 7.88, 49500),
c(176, 12.3, 10.48, 11, 7.96, 46700),
c(142, 8.2, 7.30, 5, 5.65, 32100),
c(148, 10.5, 9.61, 7, 6.15, 39150), 
c(178, 14.5, 11.05, 13, 8.06, 64700), 
c(180, 13.6, 10.40, 13, 8.47, 75700),
c(182, 12.7, 12.26, 11, 7.81, 68593), 
c(145, 14.3, 12.95, 11, 8.38, 55000),
c(161, 8.6, 8.42, 7, 5.11, 35200), 
c(117, 7.2, 6.75, 3, 5.81, 24800)
)

rownames(performanceTable) <- c(
  "Peugeot 505 GR",
  "Opel Record 2000 LS",
  "Citroen Visa Super E",
  "VW Golf 1300 GLS",
  "Citroen CX 2400 Pallas",
  "Mercedes 230",
  "BMW 520",
  "Volvo 244 DL",
  "Peugeot 104 ZS",
  "Citroen Dyane")

colnames(performanceTable) <- c(
  "MaximalSpeed",
  "ConsumptionTown",
  "Consumption120kmh",
  "HP",
  "Space",
  "Price")

# ranks of the alternatives

alternativesRanks <- c(1,2,3,4,5,6,7,8,9,10)

names(alternativesRanks) <- row.names(performanceTable)

# criteria to minimize or maximize

criteriaMinMax <- c("max","min","min","max","max","min")

names(criteriaMinMax) <- colnames(performanceTable)

x<-additiveValueFunctionElicitation(performanceTable,  
                                      criteriaMinMax, epsilon,
                                      alternativesRanks = alternativesRanks)