Analytic hierarchy process (AHP) is a well-known attribute weighting method in multi attribute decision-making. Its major requirement is to satisfy the consistency of pairwise matrix (PM).
To meet these requirements, Yang Won Chol, a researcher at the Faculty of Materials Science and Technology, proposed a new consistency improvement method of PM based on consistency ratio (CR) decreasing rate. In this method, the CR decreasing rates of all the PMs reconstituted by replacing all elements of the PM with the lower and upper neighbouring 9-point scales are calculated, and an element with maximum CR decreasing rate is found before it is modified to its lower or upper neighbouring scale.
Then, he developed a third order approximate polynomial for random consistency index by least square method. It enables determination of the RI value according to the number of attributes without a numerical table.
Finally, he proposed a final PM determination method and a final attribute weighting method with decision makers’ levels in consideration, on the basis of the CR values of individual PMs, when several decision makers perform their own pairwise comparisons.
With two numerical examples, he tested the performances of the proposed and some previous consistency improvement methods.
The results demonstrate that the proposed method improves the consistency of PM better and faster with smaller amount of modification than that of the previous methods, while it modifies the elements of the PM to 9-point scales necessarily.
He has applied the proposed method to hip joint prosthesis material selection to verify that the proposed method may be widely used in practical applications of AHP.
More information about this is found in his paper “Consistency Improvement Method of Pairwise Matrix Based on Consistency Ratio Decreasing Rate and Attribute Weighting Method Considered Decision Makers’ Levels in Analytic Hierarchy Process: Application to Hip Joint Prosthesis Material Selection” in “Mathematical Problems in Engineering” (SCI).
© 2021 KumChaek University of Technology