A Markov Chain-Based Group Consensus Method with Unknown Parameters

Abstract

Group consensus (GC) is important for generating a group solution satisfactory or acceptable to most decision-makers in a group. Its convergency usually depends on several rounds of iterations and becomes more difficult with unknown parameters because GC is usually associated with parameters. To address the GC with unknown parameters, this paper proposes a Markov chain-based GC method, in which criterion weights and expert weights are considered as parameters. Given the interval-valued assessments of decision-makers, the GC at the alternative and global levels is defined. Based on the Markov chain, a two-hierarchical randomization algorithm is designed with unknown criterion weights to determine the transition probability matrix used to generate the stable GC. To accelerate the stable GC’s convergency, criteria significantly contributing negatives to the stable GC are identified and suggestions on helping renew decision-makers’ assessments on the identified criteria are provided. On the condition that the stable GC is definitely satisfied, a GC-based two-hierarchical randomization algorithm is designed based on the Markov chain to determine the transition probability matrix for generating the stable ranking value distribution of each alternative. The proposed method is employed to analyze a development mode selection problem. It is compared with the stochastic multicriteria acceptability analysis and simple additive weighting methods based on the problem by calculation and principle.