Projection-based TOPSIS method to MAGDM in dual probabilistic linguistic information environment

Abstract

The dual probabilistic linguistic term sets (DPLTSs) are more effective than PLTSs in solving the problem of multi-attribute group decision-making (MAGDM). In this paper, an improved TOPSIS method is developed combining the TOPSIS method and projection measure of DPLTS to supplement the existing research. Firstly, considering the mathematical characteristics of DPLTS, this paper defines the concepts of the module, cosine function, and projection of DPLTS, and then proves the mathematical properties of the cosine function. Secondly, considering the uncertainty of decision-making problems, the weight-solving models are established respectively under the condition that the weight information is completely unknown and partially known. Furthermore, a novel DPLPrj-TOPSIS approach is established based on the projection measure proposed. It involves integrating experts’ DPLTS evaluations, normalizing different DPLTSs, calculating alternatives’ relative closeness and score, etc. Secondly, the proposed method’s feasibility is demonstrated through a case study that entails selecting network promotion plans for food manufacturers. Finally, the proposed method’s effectiveness and validity are verified by comparing and analyzing it with the traditional TOPSIS method based on a distance measure and other existing decision methods.