Probabilistic Linguistic Group Decision-Making Method Based on Attribute Decision and Multiplicative Preference Relations

In some cases, decision makers (DMs) need to use multiplicative linguistic terms to express evaluations, and probabilistic linguistic preference relation (PLPR) cannot meet the needs of decision makers. Multiplicative probabilistic linguistic preference relations (MPLPRs) can solve this problem. The consistency of preference relations is crucial to ensure reliable decision results. We define the ordinal consistency of MPLPRs, and improve the ordinal consistency of MPLPRs. In order to facilitate calculation, the mapping from probabilistic linguistic term set (PLTS) to linguistic term is defined. In probabilistic linguistic information decision-making methods, some methods only collect the information of the decision matrix, and some methods only collect the information of the preference matrix, and almost no decision method that uses the decision matrix and the preference relation information at the same time, but the optimal ranking of alternatives is obtained according to the comprehensive attribute of alternatives. Based on the above considerations, first, we construct a nonlinear objective optimization model containing alternative attributes and alternative preferences. Then, a probabilistic linguistic group decision-making method based on attribute decision and multiplicative preference relations is further proposed. Finally, the feasibility of the method is illustrated by an example of hospital evaluation, and the advantages of the proposed method are verified by comparing the differences between the proposed method and other methods.