A stable multi-criteria decision model based on Markov chain

This paper aims to generate a stable solution to a multi-criteria decision-making (MCDM) problem with unknown decision parameters. To this end, it proposes a multi-criteria decision model with interval numbers based on the Markov chain. For the construction of the proposed model, MCDM is demonstrated from the perspective of the Markov chain. Under these conditions, optimization problems are constructed for each alternative with a specified ranking based on unknown criterion weights, which are representative decision parameters. By using the optimized criterion weight matrix of each alternative derived from the constructed optimization problems, the transition probability of each alternative between two rankings is designed to form the transition probability matrix of each alternative. The relevant properties are theoretically analyzed. From the eigenvector of such a matrix, the stable ranking value distribution of each alternative is obtained, whose existence and uniqueness are theoretically proven. The stable solution is generated from the stable ranking distributions of alternatives. The proposed model is then used to analyze a management platform supplier selection problem, in which its applicability and validity are demonstrated. The meaningfulness of the proposed model is validated by simu-lation experiments and case comparison.

Automated summary

This paper proposes a multi-criteria decision model with interval numbers based on the Markov chain to generate a stable solution for a multi-criteria decision-making problem with unknown decision parameters. The existence and uniqueness of the stable solution are theoretically proven, and the effectiveness and applicability of the model are validated through case comparison.