A linear programming method for multiple criteria decision making with probabilistic linguistic information

The hesitant fuzzy linguistic term set (HFLTS) is applicable in expressing people's hesitant qualitative preference information. However, it may lose preference information as all the terms in the HFLTS are assigned the same weight. The probabilistic linguistic term set (PLTS) can avoid this drawback by allowing the decision makers (DMs) to give the weight of each linguistic term as a probability. Due to the flexibility of the PLTS, the multiple criteria decision making (MCDM) with probabilistic linguistic information is now becoming a hot research topic. The aim of this paper is to propose a linear programming method to solve the MCDM problems, in which the DMs' preferences over the alternatives with respect to the given criteria are expressed as the PLTSs. We first give the weighted deviation square measure for the normalized probabilistic linguistic positive ideal solution and each normalized probabilistic linguistic evaluation vector of each alternative. Then, we define the inconsistency index and the consistency index according to the objective and subjective evaluations given by the DMs, based on which a linear programming model is then built to derive the weight of each criterion. Furthermore, a linear programming method is developed to solve the MCDM problems with probabilistic linguistic information, and a case study about the evaluation of hospitals is conducted to illustrate the proposed method. Finally, some comparative analyses with the aggregation operator-based method and the probabilistic linguistic preference ranking organization method for enrichment evaluation (PL-PROMETHEE) method are made to show the advantages of the proposed method. (C) 2017 Elsevier Inc. All rights reserved.