# Title: 	Simple Analytic Hierarchy Process function
# Author: 	James Keirstead
# Date: 	5 August 2009

# Installation
# --------------------
# To install the script, copy and paste its contents into an R session
# (www.r-project.org) or load it using the "source" command.
#
# Usage
# --------------------
# To call the function, use something like:
#
# categories <- c("Apples","Oranges","Pears")
# ahp <- AHP(categories)
#
# The script will ask you to compare pairs of categories.  Answer
# each question with a clear goal in your mind (e.g. which fruit
# is tastiest) and use scores from 1,3,5,7,9 or 1, 1/3, 1/5, 1/7, 1/9
# where 1 = equal, 3 = moderately preferred, 5 = strongly preferred,
# 7 = very strongly preferred, 9 = extremely preferred.
#
# Example: If A is moderately preferred to B, answer as follows:
#
# 	Compare A to B: 3 
# or 	Compare B to A: 1/3
#
# Output
# --------------------
# Using the above example, the results can be accessed as follows:
#
# Weights of each category: 	ahp$weight
# Consistency ratio: 		ahp$cr
#
# The weights should only be used if the consistency ratio is less
# than or equal to 0.10; otherwise repeat the analysis.
#
# For more information
# --------------------
# http://www.academicproductivity.com/2009/testing-the-general-model-of-productivity

AHP <- function(x) {
      n <- length(x)
      mat <- diag(n)

      # Randomly mix the categories
      comb <- combn(x,2)
      o <- sample(1:ncol(comb))
      for (i in o) {
      	  c <- which(x==comb[1,i])
      	  r <- which(x==comb[2,i])
	  val <- readline(paste("Compare",x[r],"to",x[c]," 1-9: "))
	  mat[c,r] <- eval(parse(text=val))
       }	  

      mat <- t(mat) + mat
      mat[upper.tri(mat)] <- 1/mat[upper.tri(mat)]
      diag(mat) <- 1

      result <- eigen (mat)
		    val <- as.numeric(result$values[1])
		    vec <- as.numeric(result$vectors[,1])
		    weight <- vec /sum(vec)
		    ci <- (val-n)/(n-1)
		    cr <- ci/c(0,0,0.58,0.9,1.12,1.24,1.32,1.41,1.45,1.49,1.51,1.53)[n]
		    if (ci > 0.1 || cr > 0.1) {
		       cat("\n CI = ",ci,", CR = ", cr, "\n", sep="")
		       print(mat)
		       W <- outer(weight, weight,"/")
		       print(W)
		       print(mat-W)
		    }
		    return (list (mat=mat, lambda=val,vec=vec, weight=weight,ci=ci,cr=cr))
}