ahp.interval: A function to obtain the probabilities of rank reversals

In iaga/ahpsensitivity: Sensitivity analysis tools for Multicriteria Decision Making methods

Description

A function to obtain the probabilities of rank reversals

Usage

ahp.interval(lower, upper, nmatrices, norm_test)

Arguments

lower	A list of dataframes objects with the lower bounds for each pairwise comparison matrix
upper	A list of dataframes objects with the upper bounds for each pairwise comparison matrix
nmatrices	Integer, defines the total number of random matrices to generate
norm_test	Logical, if TRUE determines if the components of the right eigenvector of all the generated random pairwise comparison matrices are normally distributed, via the kolmogorov-smirnoff test

Value

A list of list, for each interval pairwise comparison matrix

matrix_list

List of random matrices (rm)

matrices_w

List of weight of rm

norm_matrices_w

List of normalized weights of rm

lambda_max

List of largest eigenvalues

ci

List of consistency indices

cr

List of consistency ratios

w_consistent

Dataframe of normalized weights of consistent random matrices (crm)

maximum

Named vector, maximum value of the crm for each criteria

minimum

Named vector, minimum value of the crm for each criteria

mean

Named vector, mean value of the crm for each criteria

sd

Named vector, standard deviation value of the crm for each criteria

normality

List of list with the normality test for each criteria

p_ij

Vector, probabilities of rank reversal between two alternatives A_i and A_j

p_i

Vector, probabilities that a given alternative will reverse rank with other alternative

Details

The probabilities p_i, i = 1, … , n that a given alternative will reverse rank with another alternative are given by

p_i=1-∏_{j=1}^n (1-p_{ij})

where p_{ij} is the probability of rank reversal for two alternatives, it is calculated considering different cases for the lower and upper bounds on the i and j components of the right eigenvector w and the probability cumulative distribution F_i(x_i):

Case	Condition	p_{ij}
1	w_j^L≤q w_i^L and w_i^U≤q w_j^U	F_j(w_i^U)-F_j(w_i^L)
2	w_i^L < w_j^L and w_j^U < w_i^U	F_i(w_j^U)-F_i(w_j^U)
3	w_i^L < w_j^L < w_i^U < w_j^U	(F_i(w_i^U)-F_i(w_j^L))(F_j(w_i^U)-F_j(w_j^L))
4	w_j^L < w_i^L < w_j^U < w_i^U	(F_i(w_j^U)-F_i(w_i^L))(F_j(w_j^U)-F_j(w_i^L))

References

Saaty, Thomas L. y Vargas, Luis G.: Uncertainty and rank order in the analytic hierarchy process. European Journal of Operational Research, 1987, 32(1), pp. 107–117. ISSN 0377- 2217. doi: 10.1016/0377-2217(87)90275-X.

iaga/ahpsensitivity documentation built on Dec. 20, 2021, 5:57 p.m.