The analytical hierarchy process (AHP) uses pairwise comparison matrix (PCM) to rank a known set of alternatives. Sometimes the comparisons made by the experts may be inconsistent which results in incorrect weights and rankings for the AHP. In this paper, a method is proposed which identifies inconsistent elements in a PCM and revises them iteratively until the inconsistency is reduced to an acceptable level. An error function similar to chi-square is used to identify the inconsistent elements which are revised with suitable values. The method is illustrated with some numerical examples mentioned in the literature and a comparative study of the results in terms of deviation from the PCM and preservation of original information is taken up. Monte Carlo simulation experiments over a large set of random matrices indicate that the proposed method converges for the moderately inconsistent matrices.

The importance of fuzzy numbers to express uncertainty in certain applications, concerned with decision making, is observed in a large number of problems of different kinds. In Decision making problems, the best of available alternatives is chosen to the possible extent. In the process of ordering the alternatives, ranking of fuzzy numbers plays a key role. A large volume of ranking methods, based on different features, have been available in this domain. Owing to the complicated nature of fuzzy numbers, the so far introduced methods suffered setbacks or posed difficulties or showed drawbacks in one context or other. In addition, some methods are lengthy and complicated to apply on concerned problems. In this article, a new ranking procedure based on defuzzification, stemmed from the concepts of geometric mean and height of a fuzzy number, is proposed. Finally, numerical comparisons are made with other existing procedures for testing and validation of proposed method with the support of some standard numerical examples.