Multi-objective using NSGA-2 for enhancing the consistency-matrix

Abstract

The problem of consistency matrix in Analytic Hierarchy Process (AHP) is an interesting issue. For achieving consistency in the inconsistent matrix, researchers usually change the consistent ratio (CR) and the deviation matrix. The pursuit of a minimal CR is important, since this index directly measures the consistency matrix in the AHP. While the deviation matrix should be minimal such that the original opinion of the decision makes is preserved. Ideally, the both value of CR and deviation matrix should be minimal. However, in fact those two objectives will be conflicted if both of them are optimized simultaneously. Therefore, a non-dominated Sorting Genetic Algorithm-2 (NSGA-2) for solving the multi-objective problems is considered as an appropriate approach for solving this problem. Six inconsistent AHP matrices are successfully repaired using NSGA-2.