Probability Distribution-Based Processing Model of Probabilistic Linguistic Term Set and Its Application in Automatic Environment Evaluation

The probabilistic linguistic term set (PLTS) is an effective tool for describing linguistic value in the process of decision-making. However, due to its complex structure, there remains numerous defects in utilizing the PLTS information. Therefore, by connecting the PLTS with discrete probability distribution, this study investigates a novel probability distribution-based processing model to process PLTS and further develops a practical multi-criteria decision-making (MCDM) approach for addressing automatic environmental monitoring evaluation problem. First, we propose two types of pre-processing methods to complete probability normalization. Accordingly, the normalized PLTS is represented in the form of probabilistic linguistic probability distribution (PLPD). Then, probabilistic linguistic earth-mover (PLEM) distance is constructed to measure the divergency between PLPDs, and a probabilistic linguistic probability distribution weighted mean (PLPDWM) is also developed to facilitate information fusion. On this basis, an aggregation operator-based MCDM approach is established that integrates the probability distribution-based PLTS processing methods and the proposed worst-priority weight (WPW) method. Finally, the developed approach is demonstrated by solving a practical atmospheric pollutant evaluation problem and its strengths are verified through further sensitivity analysis and comparative analysis.