A three-way decision method based on COPRAS in the weak probabilistic linguistic term set information systems

With the development and progress of technology, information becomes increasingly diverse, which poses higher demands on decision-making methods. Probabilistic linguistic term set (PLTS) is a tool that can more intuitively express the evaluations of decision makers (DMs). As a specialized form of PLTS with ignored probabilities, weak probabilistic linguistic term set (WPLTS) can describe incomplete or inaccurate evaluation information. Three-way decision (3WD) is an efficient decision-making method that reduces decision cost by adopting delayed decisions on the boundary domain. In this paper, we propose a novel 3WD method by combining 3WD with the complex proportional assessment (COPRAS) method under the WPLTS environment, named the WPLTS-3WD method. Firstly, we introduce the notion of the WPLTS information system. For a WPLTS information system, we propose a method of complementing the ignored probabilities and a new score function. Secondly, the objects are ranked by the COPRAS method. According to the ranking result, we define the dominance relation and dominance sets. Based on the dominance sets, the conditional probabilities can be estimated. By combining the conditional probabilities with relative loss functions, the expected losses will be obtained and the objects can be classified. Moreover, we propose two conversion functions that can convert real-valued and linguistic term evaluation information into PLTS evaluation information. Finally, we use the proposed WPLTS-3WD method to analyze the air quality of four cities. The rationality and advantages of our method are verified through experimental comparisons with other methods and parameter analysis.