The research for PLTS normalization method based on minimum entropy change and its application in MAGDM problem

In the problem of multiple attributes group decision making (MAGDM), the probabilistic linguistic term sets (PLTSs) is an useful tool which can be more flexible and accurate to express the evaluation information of decision makers (DMs). However, due to the lack of time or knowledge, DMs tend to provide the evaluation information by incomplete PLTSs (InPLTSs) which contain missing information. The process to estimate the missing information of InPLTSs is essential, which is called the normalization of InPLTSs. By analyzing the previous methods, the existing defect is that the original uncertainty information of InPLTS can be hardly retained after normalizing. Moreover, the literature that considers the normalization method from perspective of entropy change is absent. Thus, to overcome the shortcoming and fill the research blank, we propose two optimization models based on minimum entropy change of InPLTSs, which can remain the original uncertainty information of InPLTSs to the greatest extent. Inspired by entropy measure of PLTSs, the novel concepts related to entropy measure of InPLTS are developed. In addition, based on the novel normalization method, a decision model is constructed to solve the MAGDM problem. To verify the feasibility and superiority of the proposed method and model, a case about the selection of five-star scenic spots is given and we conduct to have comparative analysis with other methods.