A heuristic method to rank the alternatives in the AHP synthesis

This paper proposes a heuristic method (Bayesian cosine maximization method (BCCM)) to rank the alternatives in the Analytic Hierarchy Process (AHP) synthesis, based on the multiplicative AHP model, which focuses on the revision of the pair-wise comparison matrices (PCMs) and derivation of the priority vectors from the PCMs in whole hierarchy, considering both the consistency of the PCMs and total consistency. An Eight-step algorithm for the AHP synthesis is developed to how to revise the PCMs in the uncertainty context and generate the final priority vector of the alternatives, which obtains more accurate estimates of the priority vectors and provides a global AHP framework based on the multiplicative AHP model. Finally, two numerical examples and corresponding comparison with several other methods are implemented to illustrate the application and efficiency of the proposed BCCM. •Combine Bayesian statistics approach and cosine maximization method in AHP synthesis.•Focus on revision of the pair-wise comparison matrix (PCM) and derivation of the priority vector from the revised PCMs.•Develop an algorithm to generate the final priority vector of alternatives in AHP synthesis.•Provide a global AHP framework and more accurate estimates of the priority vectors derived from the PCMs.•Evaluate the feasibility and efficiency of the heuristic method regarding several measure criteria by two examples.