Multi-indexes decision-making using PL-BWM and probabilistic linguistic three-way TOPSIS methods: a case study.

Probabilistic linguistic term sets (PLTSs) provide a flexible tool to express linguistic preferences, which allow decision-makers to label linguistic information with different probabilities. In this paper, the theory of PLTSs is developed and a decision-making system based on PLTS is proposed to address multi-indexes decision-making problems. A new normalized model of probabilistic linguistic term element (PLTEs) is created by integrating three emotional factors of decision-makers (DMs), which can fully express the emotional attitude of DMs. Then a novel best-worst method (BWM) is put forward, termed PL-BWM, based on PLTS. The use of PL-BWM can fully reflects the preference information of DMs, and accurately describes the importance level of the indexes. The Jensen-Shannon divergence is used to obtain the index weights by merging PL-BWM-based subjective weights and exponential probabilistic linguistic fuzzy entropy-based objective weights. Inspired by three-way decision-making, a third middle reference point is introduced in classical two-way TOPSIS, dividing the scheme set into two parts to accurately locate the position of each scheme, which can achieve perfect results, overcoming the potentially ambiguous ranking of the classic two-way TOPSIS. The median evaluation is constructed as the third middle reference point to obtain the probabilistic linguistic three-way TOPSIS method. The practical implementation and the robustness of the new method are assessed on an optimal green suppliers of magnetic materials selection problem. A comparison of performance shows that the proposed method is logically consistent and can provide more suitable results than existing ones.