Paper:

# Improving Interval Weight Estimations in Interval AHP by Relaxations

## Masahiro Inuiguchi and Shigeaki Innan

Osaka University

1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan

From the viewpoint that the vagueness of a decision maker’s evaluation causes inconsistencies in a pairwise comparison matrix, interval weights have been estimated using the interval AHP. However, the estimated interval weights are often insufficient to express the vagueness of the decision maker’s evaluation. We propose three modified estimation methods for interval weights. The first is based on a relaxation of the optimality of estimated interval weights in the conventional method. The second employs a modified objective function and the third is based on a relaxation of the optimality with respect to the modified objective function. Two of the proposed methods include parameters with degrees of relaxation. Through numerical experiments with 100,000 pairwise comparison matrices generated from 100 true interval weight vectors, we demonstrate the advantages of the proposed methods over the conventional method, and determine the best method and the suitable degree of relaxation.

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