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

Area of Science:

• Decision Sciences
• Operations Research
• Fuzzy Systems

Background:

• Probabilistic linguistic term sets (PLTSs) offer flexibility in expressing uncertain preferences.
• Existing multi-index decision-making methods may lack precision in capturing decision-maker emotions and ranking schemes.
• The need for robust methods in complex selection problems, such as green supplier selection, is critical.

Purpose of the Study:

• To develop a novel decision-making system based on PLTSs for multi-index problems.
• To integrate decision-maker emotional factors into a normalized probabilistic linguistic term element model.
• To propose a probabilistic linguistic three-way TOPSIS method for improved scheme ranking and selection.

Main Methods:

• Development of a normalized probabilistic linguistic term element model incorporating emotional factors.
• Introduction of a probabilistic linguistic best-worst method (PL-BWM) for index weighting.
• Integration of Jensen-Shannon divergence for combining subjective and objective weights.
• Extension of TOPSIS to a three-way decision model using a median evaluation reference point.

Main Results:

• The proposed PL-BWM accurately reflects decision-maker preferences and index importance.
• The probabilistic linguistic three-way TOPSIS method overcomes ambiguity in scheme ranking compared to two-way TOPSIS.
• The developed system demonstrates logical consistency and provides superior results in a green supplier selection case study.

Conclusions:

• The novel decision-making system effectively addresses multi-index problems with uncertain linguistic information.
• Incorporating emotional factors and a three-way decision framework enhances the precision and reliability of decision-making.
• The proposed methods offer a more suitable and robust approach for complex selection tasks.