Research on Evaluation Method of Green Suppliers Under Pythagorean Fuzzy Environment

Comments 1: In the Introduction section 1, it is suggested to emphasize the green characteristics in the research problems. And, the major contribution of this research should be summarized.

Response 1: Thank you for your constructive comments. The green characteristics is obviously very important for this article. Thank you very much for bringing it up. We have made modifications to enrich the content of "green" in the introduction of the article. In addition, it is also necessary to list the main conclusions of the article in the introduction section.

Against the background of increasing global environmental awareness, the evaluation and selection of green suppliers has become the core link in the green supply chain strategy of enterprises. Green is not only reflected in the environmental management capability of suppliers, but also covers the environmental performance in the whole life cycle of product design, production and transportation. However, due to the diversity of green evaluation standards and the ambiguity of expert evaluation information, enterprises are faced with the challenge of difficult to scientifically and comprehensively evaluate green suppliers. How to effectively integrate these complex and ambiguous information and construct an evaluation system that meets the requirements of green characteristics and has practical applicability has become an urgent problem for enterprises and academics.

This paper innovatively applies Pythagorean fuzzy sets to the evaluation and selection of green suppliers, which breaks through the limitation of the expression range of traditional fuzzy sets, provides experts with richer evaluation space, and makes the evaluation results more accurate and reasonable. In addition, this paper also combines the TOPSIS sorting method to construct a green supplier evaluation model based on Pythagorean fuzzy set by fully utilizing the optimal value and the worst value in the evaluation data, which improves the objectivity and reliability of the evaluation results. At the same time, the entropy weight method is used to calculate the weight of each evaluation criterion, which reduces the influence of the subjective assignment method on the evaluation results and makes the weight distribution more scientific and reasonable. The evaluation system established in this paper is comprehensive and systematic, covering multiple dimensions such as economy, environment and society, which provides a scientific basis for the selection of green suppliers for enterprises. Finally, through the analysis and verification of actual cases, it proves the effectiveness and practicality of the method proposed in this paper, which provides strong support for the practice of green supply chain management.

Comments 2: In the Model section 3, the problem description under green supppliers selection scenario should be strengthened.

Response 2: We strongly agree with your comments. The problem description in the context of green supplier selection can provide readers with a clearer understanding of the research content of this article. It is necessary to strengthen the description of this section, thank you for providing this valuable suggestion.

In the context of green supply chain management, the selection of green suppliers is an important part of ensuring the sustainable development of enterprises. In order to assess the comprehensive performance of green suppliers more scientifically and accurately, this section constructs a green supplier evaluation model based on Pythagorean fuzzy set. The model is realized through the following steps: (1) First, we assess the importance of the experts involved in the evaluation by the management according to the company's management structure and decision-making needs. This step aims to determine the weight of each expert in the decision-making process and to ensure a reasonable integration of expert opinions. (2) Next, under the selected evaluation criteria, each expert independently evaluates the candidate green suppliers. These evaluations were converted to Pythagorean fuzzy numbers to capture uncertainty and ambiguity in the evaluation process. By applying the Pythagorean weighted arithmetic mean operator, we aggregated the evaluation opinions of multiple experts to form a Pythagorean comprehensive decision matrix. This step not only takes into account the subjective judgment of the experts, but also ensures the objectivity and fairness of the evaluation results through weight allocation. (3) Then the entropy weighting method is applied to determine the weight of each criterion and sub-criterion; (4) Finally, based on the Pythagorean comprehensive decision matrix, combined with the TOPSIS method, the positive and negative ideal solutions are selected and the weighted distances and relative closeness of each solution are calculated, and the solution with the largest relative closeness is taken as the optimal selection object.

Comments 3: In the conlusion Section 7, it must include the outlines of contributions, managerial insights, and future direction.

Response 3: Thank you for your constructive comments. The incomplete conclusion section is a huge loophole in our paper work, and we are very sorry for it. In response to your valuable feedback, we have enriched the conclusion section, added research shortcomings, management insights, and future research directions.

Contributions：This paper proves the effectiveness and superiority of this paper's model by applying the case of green supplier evaluation of Company A and by comparative analysis and validation analysis with other green supplier evaluation models. Green supply chain management is one of the important ways to promote the sustainable development of society. The research results in this paper, by promoting enterprises to pay more attention to environmental protection and social responsibility when choosing suppliers, help promote the green transformation and sustainable development of the whole industrial chain. This is of great significance for alleviating the pressure on resources and environment and promoting coordinated economic and social development. The green supplier evaluation method proposed in this paper integrates the evaluation indexes of economic, environmental and social dimensions, which helps enterprises assess their green performance and sustainable development capability more comprehensively when selecting suppliers. The application of this method will help enterprises build a greener, more efficient and sustainable supply chain system, thus enhancing their market competitiveness and social image.

Managerial insights：Although this paper has made some research progress in the field of green supplier evaluation, there are still some shortcomings. First, the research data in this paper mainly comes from theory construction and literature review, and lacks the verification and feedback of actual enterprise cases, which limits the universality and practicality of the research results to a certain extent. Secondly, although the evaluation index system in this paper covers the main aspects of economic, environmental and social dimensions as much as possible, there may still be the problem that the selection of indicators is not comprehensive enough or the allocation of weights is not reasonable enough.

Future direction: Future research can further expand and deepen from the following aspects: first, the green supplier evaluation method proposed in this paper can be verified and optimized in combination with actual enterprise cases to improve its universality and practicality. Secondly, the potential of more advanced fuzzy evaluation methods and technical tools in the field of green supplier evaluation can be explored, such as intuitionistic fuzzy set and hesitant fuzzy set. Finally, attention can be paid to the latest development trends and hot issues in the field of green supply chain management, such as carbon footprint management, circular economy, etc., in order to promote the continuous innovation and development of green supplier evaluation research.

Comments 4: The format of this manuscript should be carefully revised, for example, “Error! Reference source not found.”, Error! Bookmark not defined.; four models in the title of Figiure 1, Table 3 in line 160,etc.

Response 4: Thank you for your constructive comments. We are very sorry for the formatting error. We have systematically checked the entire article and re sorted and formatted all references using EndNote software, which conforms to the format of MDPI journals. Thank you very much for pointing out some issues on my form. We have checked all the forms and made corresponding adjustments.

Specific format modifications can be found in the manuscript.

Comments 5: The English writing should be minor improved for concise description.

Response 5: We appreciate your attention to the linguistic aspects of our manuscript. We believe clear and concise communication is crucial for scientific writing. In response, we revise our language, ensuring the fluency, accuracy, and consistency. We have carefully revised the language, taking into account sentence stricture, vocabulary choices, and tone. We believe these improvements will make our manuscript more accessible and engaging for readers. These changes will not influence the content and framework of the manuscript. We appreciate for Reviewers’warm work earnestly and hope that the correction will meet with approval.

Comments 1: The citation numbering in the article needs to be organized according to the order in which they appear. For example, in line 72, the citation for Zhang and Xu should be [10] instead of [18]. A comprehensive revision of the reference numbering throughout the document is recommended.

Response 1: Thank you for your constructive comments. We are very sorry for the formatting error. We have systematically checked the entire article and re sorted and formatted all references using EndNote software, which conforms to the format of MDPI journals.

Specific format modifications can be found in the manuscript.

Comments 2: The objective of the study, as stated in the introduction (lines 76-81), is not consistent with the abstract (lines 15-16). It is important to align these sections to provide clarity regarding the goal of the research.

Response 2: Thank you very much for your comment. We examined the abstract and introduction sections regarding the discussion of research objectives and found that there may have been some minor incidents due to differences between Chinese and English. The research objectives of the entire text have now been unified.

In order to overcome this problem, this paper innovatively applies Pythagorean fuzzy sets to the evaluation and selection of green suppliers, which breaks through the limitation of the expression range of traditional fuzzy sets, provides experts with richer evaluation space, and makes the evaluation results more accurate and reasonable. In addition, this paper also combines the TOPSIS sorting method to construct a green supplier evaluation model based on Pythagorean fuzzy set by fully utilizing the optimal value and the worst value in the evaluation data, which improves the objectivity and reliability of the evalua-tion results. At the same time, the entropy weight method is used to calculate the weight of each evaluation criterion, which reduces the influence of the subjective assignment meth-od on the evaluation results and makes the weight distribution more scientific and rea-sonable. The evaluation system established in this paper is comprehensive and systematic, covering multiple dimensions such as economy, environment and society, which pro-vides a scientific basis for the selection of green suppliers for enterprises. Finally, through the analysis and verification of actual cases, it proves the effectiveness and practicality of the method proposed in this paper, which provides strong support for the practice of green supply chain management.

Comments 3: It is recommended to include a stronger justification for the study in the introduction. The relevance of researching Pythagorean fuzzy and TOPSIS in the green supplier chain should be highlighted. There are existing studies on this topic, such as "Pythagorean Fuzzy TOPSIS Method for Green Supplier Selection in the Food Industry" (https://doi.org/10.1016/j.eswa.2023.120036), which can help contextualize and justify the necessity of this research.

Response 3:

Thank you for your constructive comments. We have made modifications to enrich the content of "green" in the introduction of the article. The paper “Pythagorean Fuzzy TOPSIS Method for Green Supplier Selection in the Food Industry” you recommended to us has greatly benefited us, which has enhanced our understanding of Pythagorean fuzzy and TOPSIS. After adding these sections, I believe it can help readers have a clearer understanding of this article.

Against the background of increasing global environmental awareness, the evaluation and selection of green suppliers has become the core link in the green supply chain strategy of enterprises. Green is not only reflected in the environmental management capability of suppliers, but also covers the environmental performance in the whole life cycle of product design, production and transportation. However, due to the diversity of green evaluation standards and the ambiguity of expert evaluation information, enterprises are faced with the challenge of difficult to scientifically and comprehensively evaluate green suppliers. How to effectively integrate these complex and ambiguous information and construct an evaluation system that meets the requirements of green characteristics and has practical applicability has become an urgent problem for enterprises and academics.

Hajiaghaei-Keshteli et al. propose that businesses integrate green and traditional crite-ria when selecting suppliers, emphasizing Green Supplier Selection (GSS) to mitigate en-vironmental impacts. They introduce a novel GSS approach for the food packaging indus-try, utilizing Pythagorean Fuzzy TOPSIS (PF-TOPSIS), and demonstrate its effectiveness and consistency through expert evaluation and sensitivity analysis.

Comments 4: The discussion lacks a cross-analysis between the results of the proposed model and the findings in the literature. Although there is an attempt at discussion in lines 298-307, it only describes what has been applied in the literature without delving into the implications for the present study. A more in-depth analysis is crucial to highlight the contributions of this research and its advancement of knowledge in the field.

Response 4: Thank you for taking the time to review my paper and providing valuable suggestions for revisions. You pointed out that there are shortcomings in the cross analysis section between the model and the literature results, which is indeed an area that we need to further strengthen. Based on your suggestion, I will focus on enhancing the depth and breadth of this section in the upcoming revisions to more clearly demonstrate the contribution and advancement of this research to the field knowledge.

Firstly, compared to intuitionistic fuzzy sets, Pythagorean fuzzy sets offer a wider range of combinations for membership and non-membership degrees, granting decision-makers greater flexibility and room during the evaluation process to express their uncertainties and fuzziness more precisely. This characteristic is evident in the case study and validation analysis of this paper, demonstrating the superiority of Pythagorean fuzzy sets in green supplier evaluation. Secondly, by utilizing the entropy weight method to determine criterion weights, we fully consider the information inherent in the data, mitigating biases stemming from sole reliance on subjective judgments, and thereby ensuring a more scientific and rational weight distribution. Compared to the previous research, our approach not only incorporates experts' subjective opinions but also integrates objective data information, enhancing the objectivity and accuracy of the evaluation results. Lastly, examining the ranking outcomes, while there are discrepancies in specific rankings between different models, the overall trends align, all effectively identifying the optimal green suppliers. This consistency not only validates the effectiveness of our proposed model but also illustrates the commonalities and differences in decision-making methods under different fuzzy environments when tackling complex multi-criteria decision-making problems.

Comments 5: The conclusion section is missing key elements:

The contributions of the study to knowledge, business practice, and society should be clearly articulated.

 Limitations of the study should be acknowledged.

 Suggestions for future research should be included.

Response 5: Thank you for your constructive comments. The incomplete conclusion section is a huge loophole in our paper work, and we are very sorry for it. In response to your valuable feedback, we have enriched the conclusion section, added research shortcomings, management insights, and future research directions.

Contributions：This paper proves the effectiveness and superiority of this paper's model by applying the case of green supplier evaluation of Company A and by comparative analysis and validation analysis with other green supplier evaluation models. Green supply chain management is one of the important ways to promote the sustainable development of society. The research results in this paper, by promoting enterprises to pay more attention to environmental protection and social responsibility when choosing suppliers, help promote the green transformation and sustainable development of the whole industrial chain. This is of great significance for alleviating the pressure on resources and environment and promoting coordinated economic and social development. The green supplier evaluation method proposed in this paper integrates the evaluation indexes of economic, environmental and social dimensions, which helps enterprises assess their green performance and sustainable development capability more comprehensively when selecting suppliers. The application of this method will help enterprises build a greener, more efficient and sustainable supply chain system, thus enhancing their market competitiveness and social image.

Managerial insights：Although this paper has made some research progress in the field of green supplier evaluation, there are still some shortcomings. First, the research data in this paper mainly comes from theory construction and literature review, and lacks the verification and feedback of actual enterprise cases, which limits the universality and practicality of the research results to a certain extent. Secondly, although the evaluation index system in this paper covers the main aspects of economic, environmental and social dimensions as much as possible, there may still be the problem that the selection of indicators is not comprehensive enough or the allocation of weights is not reasonable enough.

Future direction: Future research can further expand and deepen from the following aspects: first, the green supplier evaluation method proposed in this paper can be verified and optimized in combination with actual enterprise cases to improve its universality and practicality. Secondly, the potential of more advanced fuzzy evaluation methods and technical tools in the field of green supplier evaluation can be explored, such as intuitionistic fuzzy set and hesitant fuzzy set. Finally, attention can be paid to the latest development trends and hot issues in the field of green supply chain management, such as carbon footprint management, circular economy, etc., in order to promote the continuous innovation and development of green supplier evaluation research.

Comments 6: The formatting of the references needs correction.

There are several instances of "Error! Bookmark not defined" in the equation numbering, which must be fixed.

Ashkaz et al. (line 298) is not included in the reference list and should be added.

Citation [10] (line 302) should not include et al., as it refers to a single-author document (Calik).

In citation [25] (line 336), only the surname should be used. Additionally, in the sentence spanning lines 336-338, it is unclear whether the text refers to citation [25] or [26], and this ambiguity should be resolved.

Response 6: Thank you very much for your suggestions on the formatting of the references. We apologize for the formatting issue you mentioned. In response to the formatting problem of the references, we have re sorted them using EndNote software and adopted a format that meets MDPI requirements.

Specific format modifications can be found in the manuscript.

Comments 1: I immediately noticed that there are several errors (as you can see, there are 32 error indications in the PDF: "Error! Bookmark not defined" & "Error! Reference source not found.").

Response 1: We are very sorry for the formatting error. We have systematically checked the entire article and re sorted and formatted all references using EndNote software, which conforms to the format of MDPI journals. We have checked all the forms and made corresponding adjustments.We have revised the format of the entire article in order to comply with the standards of journal articles and facilitate readers' reading.

Specific format modifications can be found in the manuscript.

Comments 2: The conclusion is insufficient and too brief. There are no study limitations or future avenues of investigation. As such, I can only ask you to make the necessary corrections and resubmit the manuscript.

Response 2: Thank you for your constructive comments. The incomplete conclusion section is a huge loophole in our paper work, and we are very sorry for it. In response to your valuable feedback, we have enriched the conclusion section, added research shortcomings, management insights, and future research directions.

Contributions：This paper proves the effectiveness and superiority of this paper's model by applying the case of green supplier evaluation of Company A and by comparative analysis and validation analysis with other green supplier evaluation models. Green supply chain management is one of the important ways to promote the sustainable development of society. The research results in this paper, by promoting enterprises to pay more attention to environmental protection and social responsibility when choosing suppliers, help promote the green transformation and sustainable development of the whole industrial chain. This is of great significance for alleviating the pressure on resources and environment and promoting coordinated economic and social development. The green supplier evaluation method proposed in this paper integrates the evaluation indexes of economic, environmental and social dimensions, which helps enterprises assess their green performance and sustainable development capability more comprehensively when selecting suppliers. The application of this method will help enterprises build a greener, more efficient and sustainable supply chain system, thus enhancing their market competitiveness and social image.

Managerial insights：Although this paper has made some research progress in the field of green supplier evaluation, there are still some shortcomings. First, the research data in this paper mainly comes from theory construction and literature review, and lacks the verification and feedback of actual enterprise cases, which limits the universality and practicality of the research results to a certain extent. Secondly, although the evaluation index system in this paper covers the main aspects of economic, environmental and social dimensions as much as possible, there may still be the problem that the selection of indicators is not comprehensive enough or the allocation of weights is not reasonable enough.

Future direction: Future research can further expand and deepen from the following aspects: first, the green supplier evaluation method proposed in this paper can be verified and optimized in combination with actual enterprise cases to improve its universality and practicality. Secondly, the potential of more advanced fuzzy evaluation methods and technical tools in the field of green supplier evaluation can be explored, such as intuitionistic fuzzy set and hesitant fuzzy set. Finally, attention can be paid to the latest development trends and hot issues in the field of green supply chain management, such as carbon footprint management, circular economy, etc., in order to promote the continuous innovation and development of green supplier evaluation research.

Comments 3: Figure 1 is "messy". Do not place the legend above the graph. Table 5 also deserves readjustment to make it easier to read.

Response 3: We are very sorry for the issue with the images and tables, as it is a mistake that should not have occurred. We have made overall modifications to this, placing the legend below the image. We have also made changes to Tables 5, 6, and 7 for ease of reading.

Specific format modifications can be found in the manuscript.

Comments 4: I see that the format of the references is not in the correct format (with a [J][Hajiaghaei-Keshteli, 2023 #120][Hajiaghaei-Keshteli, 2023 #120][Hajiaghaei-Keshteli, 2023 #120][Hajiaghaei-Keshteli, 2023 #120][Hajiaghaei-Keshteli, 2023 #120] before the name of the Journals). Also take this opportunity to complete and reinforce your references with the most recent work developed with Fuzzys that have emerged in different areas (from engineering, to economics and management).

Response 4: Thank you for your constructive comments. We are very sorry for the formatting error. We have systematically checked the entire article and resorted and formatted all references using EndNote software, which conforms to the format of MDPI journals. We have strengthened the theoretical support for this article, such as studying “Pythagorean Fuzzy TOPSIS Method for Green Supplier Selection in the Food Industry”, which has enhanced our understanding of Pythagorean fuzzy and TOPSIS. After adding these sections, I believe it can help readers have a clearer understanding of this article.

Hajiaghaei-Keshteli et al. propose that businesses integrate green and traditional crite-ria when selecting suppliers, emphasizing Green Supplier Selection (GSS) to mitigate en-vironmental impacts. They introduce a novel GSS approach for the food packaging indus-try, utilizing Pythagorean Fuzzy TOPSIS (PF-TOPSIS), and demonstrate its effectiveness and consistency through expert evaluation and sensitivity analysis.

Against the background of increasing global environmental awareness, the evaluation and selection of green suppliers has become the core link in the green supply chain strategy of enterprises. Green is not only reflected in the environmental management capability of suppliers, but also covers the environmental performance in the whole life cycle of product design, production and transportation. However, due to the diversity of green evaluation standards and the ambiguity of expert evaluation information, enterprises are faced with the challenge of difficult to scientifically and comprehensively evaluate green suppliers. How to effectively integrate these complex and ambiguous information and construct an evaluation system that meets the requirements of green characteristics and has practical applicability has become an urgent problem for enterprises and academics.