Pythagorean Linguistic Information-Based Green Supplier Selection Using Quantum-Based Group Decision-Making Methodology and the MULTIMOORA Approach

Engineering Artificial Intelligence Environmental Engineering Information Science Computer Science
Pythagorean Linguistic Set MULTIMOORA Quantum Probability Theory Multi-Criteria Group Decision-Making Green Supplier Selection

With the increasing severity of global environmental issues, companies are placing greater emphasis on green and sustainable development in supply chain management. Green Supply Chain Management (GSCM) has become a crucial means for enterprises to enhance competitiveness and achieve sustainable development. However, Green Supplier Selection (GSS) is a complex Multicriteria Group Decision-Making (MCGDM) problem, involving diverse opinions and uncertainties from multiple decision-makers. Traditional MCGDM methods fall short in addressing the trustworthiness and ambiguity of expert opinions, making it difficult to accurately reflect the complexities of real-world scenarios.

To address this issue, scholars such as Prasenjit Mandal proposed a Green Supplier Selection method based on Pythagorean Linguistic Information (PLI), integrating Quantum Decision Theory (QDT) and the MULTIMOORA method to better handle the ambiguity and interference effects of expert opinions. This method introduces Pythagorean Linguistic Numbers (PLNs) to express experts’ confidence levels and uncertainties, combining them with Quantum-Scenario-Based Bayesian Networks (QSBN) and Deng entropy to quantify the interference effects of expert opinions.

Source of the Paper

The paper was co-authored by Prasenjit Mandal, Leo Mrsic, Antonios Kalampakas, Tofigh Allahviranloo, and Sovan Samanta, and published in the 2025 issue of the journal Artificial Intelligence Review. Prasenjit Mandal and Sovan Samanta are affiliated with research institutions in India, Leo Mrsic and Antonios Kalampakas are from research institutions in Croatia and Greece, respectively, and Tofigh Allahviranloo is from a research institution in Iran. The DOI of the paper is 10.1007/s10462-025-11205-x.

Research Process and Results

1. Research Process

The main steps of the research include the following:

a) Determining Criterion Weights

First, the researchers used the Pearson correlation coefficient to calculate the correlations between criteria and determine the criterion weights based on these correlations. This method avoids subjective biases and ensures the objectivity of the weights. Specifically, the researchers calculated the correlation coefficients of each criterion with others, ultimately obtaining the criterion weights for each expert.

b) Calculating First-Layer Probabilities

Next, the researchers used Shannon entropy and the relative proximity method to calculate the first-layer probabilities for each expert. Specific steps included constructing a normalized weighted decision matrix, calculating entropy values, and determining expert weights based on entropy. This step ensured a more reasonable allocation of expert opinion weights.

c) Calculating Second-Layer Probabilities

After determining the first-layer probabilities, the researchers used the MULTIMOORA method to calculate the second-layer probabilities for each expert. The MULTIMOORA method includes three sub-methods: the Ratio System (RS), the Reference Point (RP), and the Full Multiplicative Form (FMF). Through these methods, the researchers obtained the evaluation results of each expert for each alternative.

d) Comprehensive Probabilities Considering Interference Effects

Finally, the researchers used Quantum Decision Theory (QDT) and Deng entropy to quantify the interference effects between expert opinions and calculate the comprehensive probabilities for each alternative. Specifically, the researchers calculated the phase angles between expert opinions and used Deng entropy to quantify the interference effects, ultimately obtaining the comprehensive probabilities for each alternative.

2. Main Results

a) Criterion Weights

The researchers calculated the correlations between criteria using the Pearson correlation coefficient and determined the criterion weights for each expert. The results showed significant differences in the weight allocations of criteria among experts, reflecting diverse viewpoints and preferences.

b) First-Layer Probabilities

Using Shannon entropy and the relative proximity method, the researchers calculated the first-layer probabilities for each expert. The results indicated a more reasonable allocation of weights among experts, avoiding the influence of subjective biases.

c) Second-Layer Probabilities

Using the MULTIMOORA method, the researchers obtained the evaluation results of each expert for each alternative. The results showed some differences in the rankings of alternatives across methods, but overall, they reflected the strengths and weaknesses of the alternatives.

d) Comprehensive Probabilities

Through Quantum Decision Theory and Deng entropy, the researchers quantified the interference effects between expert opinions and calculated the comprehensive probabilities for each alternative. The results showed significant changes in the rankings of alternatives when interference effects were considered, reflecting the mutual influence of expert opinions.

3. Conclusion

The study proposed a Green Supplier Selection method based on Pythagorean Linguistic Information, integrating Quantum Decision Theory and the MULTIMOORA method to successfully address the ambiguity and interference effects of expert opinions. The results demonstrated that this method can more accurately reflect the complexities of real-world scenarios, providing effective decision support for Green Supply Chain Management.

4. Research Highlights

  • Novelty: This study is the first to combine Pythagorean Linguistic Information with Quantum Decision Theory, proposing a new Green Supplier Selection method.
  • Practicality: The method effectively handles the ambiguity and interference effects of expert opinions, providing a practical decision-making tool for Green Supply Chain Management.
  • Scientific Rigor: By introducing Deng entropy and Quantum-Scenario-Based Bayesian Networks, the researchers successfully quantified the interference effects between expert opinions, enhancing the scientific rigor of decision-making.

Value and Significance of the Paper

The paper provides a new decision-making method for Green Supply Chain Management, effectively addressing the ambiguity and interference effects of expert opinions. This method not only holds significant theoretical value but also offers practical tools for real-world applications. By introducing Quantum Decision Theory and Deng entropy, the researchers successfully enhanced the scientific rigor and accuracy of decision-making, providing new directions for future research.

Additionally, the study demonstrated the potential of Pythagorean Linguistic Information in Multicriteria Group Decision-Making, offering new insights for related fields. Future research can further explore the application of this method in other domains and attempt to integrate more advanced technologies to improve decision-making efficiency and accuracy.

Other Valuable Information

The study also showcased the potential of Quantum Decision Theory in group decision-making, providing new directions for future research. By introducing Deng entropy and Quantum-Scenario-Based Bayesian Networks, the researchers successfully quantified the interference effects between expert opinions, enhancing the scientific rigor of decision-making. This method is not only applicable to Green Supply Chain Management but can also be applied to other complex group decision-making problems.

The study provides a new decision-making method for Green Supply Chain Management, holding significant theoretical and practical value. Future research can further explore the application of this method in other domains and attempt to integrate more advanced technologies to improve decision-making efficiency and accuracy.