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This study introduces a new method for handling incomplete probabilistic linguistic term sets (InPLTSs) in group decision making. The approach minimizes entropy change during normalization, preserving original uncertainty for better decision analysis.

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Area of Science:

  • Decision Sciences
  • Operations Research
  • Information Systems

Background:

  • Probabilistic linguistic term sets (PLTSs) are valuable for multiple attribute group decision making (MAGDM), offering flexibility in expressing decision maker (DM) evaluations.
  • Decision makers often provide incomplete PLTSs (InPLTSs) due to time or knowledge constraints, necessitating a normalization process to estimate missing information.
  • Existing normalization methods for InPLTSs often fail to preserve the original uncertainty information and lack consideration of entropy changes.

Purpose of the Study:

  • To address the limitations of current InPLTS normalization techniques by proposing a method that maximally retains original uncertainty.
  • To introduce novel concepts for entropy measurement of InPLTSs and explore normalization from an entropy change perspective.
  • To develop a MAGDM decision model utilizing the proposed normalization method.

Main Methods:

  • Developed two optimization models based on the principle of minimum entropy change for normalizing InPLTSs.
  • Introduced novel entropy measures specifically designed for InPLTSs.
  • Constructed a MAGDM decision model incorporating the new normalization approach.

Main Results:

  • The proposed optimization models effectively normalize InPLTSs while preserving the maximum amount of original uncertainty.
  • The developed entropy measures provide a new perspective for analyzing uncertainty in incomplete linguistic information.
  • A case study on selecting five-star scenic spots demonstrated the feasibility and superiority of the proposed method compared to existing approaches.

Conclusions:

  • The minimum entropy change approach offers a superior method for normalizing InPLTSs in MAGDM problems.
  • The proposed method enhances the accuracy and reliability of decision-making processes involving incomplete linguistic information.
  • This research fills a gap in the literature by considering entropy changes in the normalization of InPLTSs.