sensitivity {AHPtools}

Compute Sensitivity

Description

This function returns a sensitivity measure for an input pairwise comparison matrix, PCM. Sensitivity is measured by Monte Carlo simulation of 500 PCMs which are perturbations of the input PCM. The perturbation algorithm makes a random choice from one of the 5 closest items in the Fundamental Scale {1/9, 1/8, ..... 1/2, 1, 2, ..... 8, 9} for each element in the PCM, ensuring the the pairwise reciprocity is maintained. The sensitivity measure is the average Spearman's rank correlation of the vector of ranks of the principal eigenvectors of (i) the input PCM and (ii) the perturbed PCM. The average of the 500 such rank correlations is reported as the measure of sensitivity.

Usage

sensitivity(PCM, typePCM = TRUE, granularityLow = TRUE)

Arguments

PCM

A pairwise comparison matrix

typePCM

boolean flag indicating if the first argument is a PCM or a vector of upper triangular elements

granularityLow

The Scale for pairwise comparisons; default (TRUE) is the fundamental scale; else uses a more find grained scale, derived from pairwise ratios of the elements of the Fundamental Scale.

Value

The average Spearman's rank correlation between the principal eigenvectors of the input and the perturbed 'PCMs'

Examples

revcons1 <- revisedConsistency(matrix(
                 c(1,1/4,1/4,7,1/5, 4,1,1,9,1/4, 4,1,1,8,1/4,
                 1/7,1/9,1/8,1,1/9, 5,4,4,9,1), nrow=5, byrow=TRUE))
revcons1
sensitivity2 <- sensitivity(matrix(
                 c(1,7,1,9,8, 1/7,1,1/6,7,9, 1,6,1,9,9, 1/9,1/7,1/9,1,5,
                 1/8,1/9,1/9,1/5,1), nrow=5, byrow=TRUE))
sensitivity2