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A method to dynamic stochastic multicriteria decision making with log-normally distributed random variables.

Xin-Fan Wang1, Jian-Qiang Wang, Sheng-Yue Deng

  • 1School of Science, Hunan University of Technology, Zhuzhou 412007, China ; School of Business, Central South University, Changsha 410083, China.

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Summary

This study introduces a new method for dynamic stochastic multicriteria decision making (SMCDM) problems involving log-normally distributed variables. The approach uses novel geometric operators for improved decision analysis and alternative selection.

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Area of Science:

  • Decision Analysis
  • Stochastic Processes
  • Operations Research

Background:

  • Dynamic stochastic multicriteria decision making (SMCDM) problems often involve complex data distributions.
  • Log-normally distributed random variables present unique challenges in aggregation and analysis.
  • Existing methods may not adequately address the dynamic and stochastic nature of these criteria.

Purpose of the Study:

  • To develop a novel method for solving dynamic SMCDM problems with log-normally distributed criterion values.
  • To introduce new aggregation operators specifically designed for log-normal distributions.
  • To provide a robust framework for ranking and selecting alternatives under uncertainty.

Main Methods:

  • Proposed two new geometric aggregation operators: the log-normal distribution weighted geometric (LNDWG) operator and the dynamic log-normal distribution weighted geometric (DLNDWG) operator.
  • Developed a decision-making method utilizing these operators to aggregate log-normally distributed criterion values.
  • Employed Shannon's entropy model to generate time weights and used expectation values and variances for ranking alternatives.

Main Results:

  • The developed method effectively aggregates log-normally distributed criterion values using the LNDWG and DLNDWG operators.
  • The method successfully ranks alternatives by considering expectation values and variances.
  • A practical example demonstrated the feasibility and effectiveness of the proposed approach.

Conclusions:

  • The new method provides an effective solution for dynamic SMCDM problems with log-normal distributions.
  • The introduced DLNDWG and LNDWG operators enhance the analysis of stochastic multicriteria decisions.
  • This research offers a valuable tool for decision-making in complex, uncertain environments.