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

Analytic hierarchy process (AHP) is a well-known attribute weighting method in multiattribute decision-making. Its major requirement to satisfy the consistency of pairwise matrix (PM). To solve this problem, we first propose new improvement PM based on ratio (CR) decreasing rate. In method, calculate CR rates all PMs reconstituted by replacing elements with lower and upper neighbouring 9-point scales find element maximum rate, then modify it its or scale. Second, develop third-order approximate polynomial for random index using least square method. It enables determine RI value according number attributes without numerical table. Third, final determining considered decision makers’ levels values individual case several makers perform their own comparisons. We test performances proposed some previous methods two examples. The results demonstrate that improves better faster smaller amount modification than methods, while scales, necessarily. apply hip joint prosthesis material selection. may be widely used practical applications AHP.