Genetic algorithm optimised Hadamard product method for inconsistency judgement matrix adjustment in AHP and automatic analysis system development

Abstract

The analytic hierarchy process (AHP) is an important method to solve the multi-objective decision-making weight problem. However, due to the subjective judgement and selection preference of decision-makers, the consistency of the judgement matrix is inevitably poor. Hence, to improve the reliability of decision-making results, it is necessary to adjust the consistency of the judgement matrix. We propose a genetic algorithm optimised Hadamard product (GAOHP) to judge the consistency of the matrix. This method converts the original matrix consistency adjustment problem into an optimisation solution problem and uses a meta-heuristic algorithm to search the global optimisation quickly. Our method, which significantly improves the computing efficiency and realises that the judgement matrix after adjustment satisfies the basic consistency, has fully retained the judgement intention of the decision-makers. It offers the dual advantages of preserving the original intention of decision-makers and greater efficiency of operation. Finally, we developed an automatic analysis system based on MATLAB app designer to realise the rapid adjustment of the consistency of judgement matrix, which is conducive to providing an analysis system with simple and stable operation for AHP analysis.