Integrating the Coupled Markov Chain and Fuzzy Analytic Hierarchy Process Model for Dynamic Decision Making

Abstract

This paper introduces a pioneering model that merges coupled Markov chains (CMC) with the fuzzy analytic hierarchy process (FAHP) to enhance multi-criteria decision making (MCDM) amidst the dynamic interplay of criteria. Traditional MCDM frameworks often lack the granularity to manage the intricate and changing relationships among criteria. Our model addresses this gap by integrating fuzzy numbers into AHP, providing a nuanced means to handle the inherent uncertainty of decision criteria. The application of the Kronecker product in CMC enriches our approach, offering a data-driven analysis while mitigating excessive dependence on subjective expert opinion. A comprehensive numerical example underlines the model’s improved decision-making accuracy and efficiency, marking a substantial advancement in MCDM methodologies. This research contributes to the field by presenting a sophisticated yet practical framework for dynamic decision analysis in complex uncertain environments.

Keywords

• multi-criteria decision making
• coupled Markov chains
• fuzzy analytic hierarchy process
• dynamic decision analysis
• Kronecker product