# Analytic Hierarchy Process (AHP) method AHP is a multi-criteria decision analysis method which was originally developed by Thomas L. Saaty in 1970s. ```r AHP(criteriaWeightsPairwiseComparisons, alternativesPairwiseComparisonsList) ``` ## Arguments - `criteriaWeightsPairwiseComparisons`: Matrix or data frame containing the pairwise comparison matrix for the criteria weights. Lines and columns are named according to the IDs of the criteria. - `alternativesPairwiseComparisonsList`: A list containing a matrix or data frame of pairwise comparisons (comparing alternatives) for each criterion. The elements of the list are named according to the IDs of the criteria. In each matrix, the lines and the columns are named according to the IDs of the alternatives. If one criteria is already a score (i.e. it is a numeric value between 0 and 1 where higher values indicate better performance), then providing a nAlt-length vector, or a nAlt x 1 matrix containing the score associated with each alternative will be enough, but the vector or rows of the matrix must be named as the alternatives. ## Returns The function returns a vector containing the AHP score for each alternative. ## Examples ```r alts <- c("Corsa","Clio","Fiesta","Sandero") style <- matrix(c(1.0, 1/4, 4.0, 1/6, 4.0, 1.0, 4.0, 1/4, 1/4, 1/4, 1.0, 1/5, 6.0, 4.0, 5.0, 1.0), nrow=length(alts), ncol=length(alts), byrow=TRUE, dimnames=list(alts,alts)) reliability <- matrix(c(1.0, 2.0, 5.0, 1.0, 1/2, 1.0, 3.0, 2.0, 1/5, 1/3, 1.0, 1/4, 1.0, 1/2, 4.0, 1.0), nrow=length(alts), ncol=length(alts), byrow=TRUE, dimnames=list(alts,alts)) fuel <- matrix(c(1.0, 2.0, 4.0, 1.0, 0.5, 1.0, 3.0, 2.0, 1/4, 1/3, 1.0, 1/5, 1.0, 1/2, 5.0, 1.0), nrow=length(alts), ncol=length(alts), byrow=TRUE, dimnames=list(alts,alts)) alternativesPairwiseComparisonsList <- list(style = style, reliability = reliability, fuel = fuel) crit <- c("style","reliability","fuel") criteriaWeightsPairwiseComparisons <- matrix(c(1.0, 1/2, 3.0, 2.0, 1.0, 4.0, 1/3, 1/4, 1.0), nrow=length(crit), ncol=length(crit), dimnames=list(crit,crit)) # All attributes have pairwise comparisons AHP(criteriaWeightsPairwiseComparisons, alternativesPairwiseComparisonsList) # Fuel is a score newFuel <- c(Corsa=34, Clio=27, Fiest=24, Sandero=28) newFuel <- newFuel/sum(newFuel) alternativesPairwiseComparisonsList$fuel <- newFuel AHP(criteriaWeightsPairwiseComparisons, alternativesPairwiseComparisonsList) ``` ## References The Analytic Hierarchy Process: Planning, Priority Setting (1980), ISBN 0-07-054371-2, McGraw-Hill

AHP function