Using GNU R in AHP

Scenario:

• The goal is to select the most appropriate sedan from the candidates.
• Selection criterion are:
  • Style
  • Reliability
  • Fuel Consumption
  • Price
• Criterion Comparison Table:

• Style Comparison Table:

• Reliability Comparison Table:

• Owing to Fuel Consumption and Cost are both Quantitative criterion, there are no needs of comparison tables for such criterion.

GNU R:

• It is very powerful programmable statistical tool. This material is to demonstrate how GNU R can facilitate the Analytical Hierarchy Process (AHP) in decision making.

• In order to facilitate the calculation during AHP, a function library is designed as follows:
  • ahp_dot <- function(m) {
  • m -> ret
  • for (i in 1:length(m[1,])) {
  • for (j in 1:length(m[,1])) {
  • sum(m[i,] * m[,j]) -> ret[i,j]
  • }
  • }
  • ret
  • }
  • ahp_eigen_vector <- function(m) {
  • m[1,] -> ret
  • for (i in 1:length(m[1,])) {
  • sum(m[i,]) -> ret[i]
  • }
  • ret
  • }
  • ahp_weight <- function(v) {
  • sum(v) -> total
  • v -> ret
  • for (i in 1:length(v)) {
  • v[i]/total -> ret[i]
  • }
  • ret
  • }
  • ahp_eigen <- function(m) {
  • ahp_weight(ahp_eigen_vector(ahp_dot(m))) -> ret
  • ret
  • }
  • ahp_eigen_check <- function(v1, v2) {
  • v1 - v2 -> ret
  • ret
  • }
  • ahp_process <- function(m) {
  • ahp_dot(m) -> my_dot
  • ahp_eigen(my_dot) -> ret
  • ret
  • }
• Main R program is as follows:
  • read.table("AHP-Criteria-Weight.dat") -> my_data
  • ahp_process(my_data) -> my_eigen
  • read.table("AHP-Style-Comparison.dat") -> my_data_1
  • ahp_process(my_data_1) -> my_eigen_1
  • read.table("AHP-Reliability-Comparison.dat") -> my_data_2
  • ahp_process(my_data_2) -> my_eigen_2
  • read.table("AHP-Fuel-Comparison.dat") -> my_data_3
  • ahp_weight(my_data_3[1,]) -> my_eigen_3
  • read.table("AHP-Price-Comparison.dat") -> my_data_4
  • ahp_weight(my_data_4[1,]) -> my_eigen_4
  • matrix(c(my_eigen_1, my_eigen_2, my_eigen_3), length(my_eigen_3)) -> my_matrix
  • my_eigen_3 -> ret
  • for (i in 1:length(my_eigen_3)) {
  • sum(my_matrix[i,] * my_eigen) -> ret
  • }
  • print(ret * my_eigen_4)
• Weight of Criteria Table:

• Weight Table of Candidates:

• Benefit Comparison Table:

• The best choice is Civic, and the worst one is Clio.