An interval-valued linguistic Markov decision model with fast convergency

To rapidly generate stable solutions to the interval-valued linguistic decision-making problems, this paper proposes a novel interval-valued linguistic Markov decision model with fast convergency. A mapping framework is constructed to associate an interval-valued linguistic decision-making problem with a Markov chain. In consideration of two types of decision parameters including criterion weight and criterion reliability, two pairs of optimization problems are constructed under the framework to determine the optimized criterion weight interval and criterion reliability interval. A similarity measure between two rectangles formed by two pairs of optimized criterion weight and criterion reliability intervals is defined, and its relevant properties are theoretically proven. Based on the similarity measure, the transition probability of an alternative from one interval-valued linguistic term into another is constructed from the abstract combination of the developed similarity measure and an adaption parameter for fast convergency. The second largest eigenvalue modulus is then minimized to accelerate the generation of stable solutions, in which the corresponding adaption parameter is determined. The proposed decision model is used to help select suppliers of enterprise resource planning system for an enterprise that manufactures the key parts of high-speed trains, in which its applicability and validity are demonstrated. The necessity of the proposed decision model is further highlighted by comparative experiments.