Cognition-driven linguistic decision-making method based on maximum entropy rate Markov chain

In existing linguistic decision-making (LDM) methods, individual decision maker generally evaluates alternatives through a single-round evaluation process, in which only preliminary cognition of individual decision maker can be excavated. This results in the evaluation provided by individual decision maker may not well reflect their integrated preference through the single-round evaluation process. To address this issue, a multi-round evaluation process should be designed, in which the decision maker can constantly renew his or her acquired cognition through previous rounds of evaluation and further updates his or her evaluation. In this paper, a cognitive-driven LDM method based on the multi-round evaluation process is proposed to overcome the insufficiency of existing methods in adequately exploring the decision maker comprehensive cognition. First, the transition process of linguistic term (LT) of the alternative induced by decision maker’s cognition renewal is modeled as a Markov chain. The transition probability from one state to another within the state space is then created to obtain the incomplete transition matrix, whose entropy rate is maximized to derive the complete transition matrix via the constructed convex optimization problem. The stable distributions of alternatives can be generated based on their complete transition matrices. The aggregated stable distributions of alternatives are obtained by minimizing the dissimilarity between them and the individual stable distributions of alternatives on the criteria. On this basis, the ranking order of alternatives can be generated. The proposed method is further applied to a diagnostic ultrasound system selection problem for demonstrating its applicability and effectiveness. The comparative experiment reveals the significance of considering decision maker’s renewal cognition in the multi-round decision-making process. This paper provides insights on improving decision-making quality through the modeling of decision maker's acquired cognition in the multi-round decision-making processes.