Centre for Operational Research and Logistics
Events and Seminars
On the proper fuzzification of the AHP method
The Analytic Hierarchy Process is a multricriteria decision making method utilized to cope with complex problems using pairwise comparison matrices of objects. A linguistic scale is used for expressing the intensities of preferences while comparing the objects pairwisely. Each linguistic term from the scale is described by a real number. However, in real world, the intensities of preferences are usually vague. Therefore, fuzzy numbers are more suitable for their description. Many proposals of the fuzzification of the AHP method have appeared in the literature. Usually, triangular fuzzy numbers are used. First of all, the fuzzification of the linguistic scale has to be done properly paying attention especially to the fuzzification of the number 1 staying for the equal preference.
In the classic AHP, the Geometric mean method and the Eigenvector method are the basic methods for obtaining the weights of objects from pairwise comparison matrices. Fuzzification of these methods has been proposed in the literature. However, the fuzzified form of these methods has several drawbacks regarding the violation of the reciprocity condition of the fuzzy pairwise comparison matrices. Therefore, revision of these method by applying the reciprocity condition is need. The fuzzy weights obtained by the revised formulas are then less vague since all unfeasible combinations of the elements from the fuzzy matrix are eliminated, and they represent the actual weights of the objects. Similarly, also the fuzzification of the weighted average for obtaining the overall weights of the alternatives has to be done properly preserving the reciprocity of fuzzy pairwise comparison matrices.
Jana Krejci, Universtity of Trento, Italy
Dennis Sciama Building, DS 1.04
Date and Time
Wed, 26 Nov 2014, 13:15 - 15:00 (BST)
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