Multi-Criteria Decision-Making Method Based on Complex t-Spherical Fuzzy Aczel–Alsina Aggregation Operators and Their Application
Round 1
Reviewer 1 Report
The article is a structured manuscript with reasonably well flow. However, the following observations are made herein for further improving the quality of the paper.
1. Please strengthen the literature review while explaining the research rational. Author may include the following
https://link.springer.com/article/10.1007/s00521-020-05623-x
2. Author should reduce the preliminary section or put the basic mathematical section into "Appendix".
3. Case study is not convincing.
4. Connect discussions, research gaps and future research scope more elaborately for better understanding.
5. The expression of validation and sensitivity analysis could have been better.
Author Response
Referee: 1
The article is a structured manuscript with reasonably well flow. However, the following observations are made herein for further improving the quality of the paper.
Comment 1: Please strengthen the literature review while explaining the research rational. Author may include the following
https://link.springer.com/article/10.1007/s00521-020-05623-x
Reply: We have strengthen the literature review by adding some more recent articles, specifically the suggested ones.
Comment 2: Author should reduce the preliminary section or put the basic mathematical section into "Appendix".
Reply: We have reduced the preliminary section as per your valuable suggestion.
Comment 3: Case study is not convincing.
Reply: Our work is on complex t-spherical fuzzy set, which was designed to work with two dimensional data. The considered study a company X needs to purchase automobiles from a car manufacturer Y, which provides information on (1) vehicle models and (2) vehicle production dates. The data is therefore two-dimensional. Consequently, it is preferable to address similar situations with complex fuzzy sets.
Comment 4: Connect discussions, research gaps and future research scope more elaborately for better understanding.
Reply: It has been done accordingly.
Comment 5: The expression of validation and sensitivity analysis could have been better.
Reply: We totally agree with your valuable comment.
Reviewer 2 Report
Dear Authors,
The main objective of submitted paper is to propose complex t-spherical fuzzy decision making methodology based on Aczel–Alsina operations, and entropy measure to rank vehicle models. The proposed approach also makes it possible to determine the weights of the criteria without the necessity of the participation of decision-makers.
- The topic of the paper is up-to-date and significant.
- The proposed method is extensively explained and well presented.
- The article has a strong methodological contribution that has practical applications.
- The article is mainly focused on the novel methodology which is introduced.
- The Introduction dedicates too little space to general information about MCDM methods, which may be helpful for readers unfamiliar with MCDM methods.
- The significance of the problems considered is supported by relevant literature.
- The article's contribution is well justified.
- On page 8 of the manuscript, the term Aszel-Alsina appears for the first time. The Authors should introduce the reader to this concept more broadly earlier, for example, in the Introduction, since only the concept of Aczel-Alsina has been described so far. It is also recommended to include literature references to Aszel-Alsina.
- On page 18 of the manuscript, in line 1 of Theorem 9, it looks like part of the equation did not fit on the line and is not continued in the following line. The Authors should revise it.
- Practical example is well descibed and clearly demonstrated.
- Figures and tables are clear and easy to interpret.
- On page 33 of the manuscript, in line 8, the name of the TOPSIS method is mentioned twice ([55] and [56]). References are not a sufficient explanation of this issue. It should be clarified in the manuscript's text at this point exactly which extensions of the TOPSIS method are involved. It should also be clarified in the manuscript's text what the two types of TOPSIS methods are and the differences between them.
- The comparative analysis between the proposed method and the reference approach is interesting and contributes significantly to work.
- The Authors should explain why the TOPSIS method was chosen for this comparative analysis and not another MCDM method.
- Please explain what the Failed score in Table 5 means for the TOPSIS methods compared, why the scores for S(M1)-S(M4) were not obtained for these methods, and why the score for them is Failed.
Author Response
Referee: 2
The main objective of submitted paper is to propose complex t-spherical fuzzy decision making methodology based on Aczel–Alsina operations, and entropy measure to rank vehicle models. The proposed approach also makes it possible to determine the weights of the criteria without the necessity of the participation of decision-makers.
Comment 1: The topic of the paper is up-to-date and significant.
Reply: Thank you for adding this valuable comment on our research.
Comment 2: The proposed method is extensively explained and well presented.
Reply: Thank you once again.
Comment 3: The article has a strong methodological contribution that has practical applications.
Reply: Many thanks for appreciation.
Comment 4: The article is mainly focused on the novel methodology which is introduced.
Reply: Thanks a lot for adding this valuable comment regarding our research.
Comment 5: The Introduction dedicates too little space to general information about MCDM methods, which may be helpful for readers unfamiliar with MCDM methods.
Reply: As per your valuable suggestion, we have added more literature to the introduction section.
Comment 6: The significance of the problems considered is supported by relevant literature.
Reply: Thanks a lot for this worthy comment.
Comment 7: The article's contribution is well justified.
Reply: Thanks for appreciation.
Comment 8: On page 8 of the manuscript, the term Aszel-Alsina appears for the first time. The Authors should introduce the reader to this concept more broadly earlier, for example, in the Introduction, since only the concept of Aczel-Alsina has been described so far. It is also recommended to include literature references to Aszel-Alsina.
Reply: We completely agree with your suggestion. The manuscript has been revised accordingly.
Comment 9: On page 18 of the manuscript, in line 1 of Theorem 9, it looks like part of the equation did not fit on the line and is not continued in the following line. The Authors should revise it.
Comment 10: Practical example is well descibed and clearly demonstrated.
Reply: Many thanks for your positive comment.
Comment 11: Figures and tables are clear and easy to interpret.
Reply: Thank you once again.
Comment 12: On page 33 of the manuscript, in line 8, the name of the TOPSIS method is mentioned twice ([55] and [56]). References are not a sufficient explanation of this issue. It should be clarified in the manuscript's text at this point exactly which extensions of the TOPSIS method are involved. It should also be clarified in the manuscript's text what the two types of TOPSIS methods are and the differences between them.
Reply: TOPSIS ([55] and [56]), which are now [58] and [59] (in the revised version) both are complex spherical fuzzy extensions of TOPSIS method. The primary processes of both references are identical, but [59] takes initial data in the form of linguistic terms and evaluates the linguistic significance of criteria. On the other hand, [58] considered the weights of criterion to be totally known and utilized Bonferroni aggregation operators to create the collective decision matrix.
Comment 13: The comparative analysis between the proposed method and the reference approach is interesting and contributes significantly to work.
Reply: Thank you for your kind words.
Comment 14: The Authors should explain why the TOPSIS method was chosen for this comparative analysis and not another MCDM method.
Reply: Due to the fact that very few studies have been conducted in the complex t-spherical fuzzy setting to date. To strengthen the comparative section, we must compare our work with more methodologies. We have therefore included, in addition to aggregation operators, the complex spherical fuzzy TOPSIS approach.
Comment 15: Please explain what the Failed score in Table 5 means for the TOPSIS methods compared, why the scores for S(M1)-S(M4) were not obtained for these methods, and why the score for them is Failed.
Reply: Because these methods are restricted to the condition 0 ≤ (ð µ )^2+ (ð ϑ )^2+ (ð ν )^2 ≤ 1. Please refer to Section 7 , para nu 4.
Reviewer 3 Report
Since the proofs are so complexed, they should be simplified and readibility of the manuscript should be easier.
Author Response
Referee: 3
Comment 1: Since the proofs are so complexed, they should be simplified and readibility of the manuscript should be easier.
Reply: As per your valuable suggestion, we have replaced the complicated notations by simpler ones in order to make the readability of the manuscript easy.
Reviewer 4 Report
The paper entitled "Multi-criteria decision-making method based on complex t-spherical fuzzy Aczel-Alsina aggregation operators and its application" is an interesting article. I have been through the paper, and the results produced in the paper are novel. A few suggestions are given below for the improvement of the paper.
1. Please discuss the significance of complex t-spherical fuzzy sets in the abstract.
2. The introduction should add more recent and relevant literature on T-spherical fuzzy sets and Aczel Alsina aggregation operators.
3. I can see the author referred to [20] in lines 4th and 5th lines of page 3. Here the most suitable reference is [50] here at this place.
4. The author is suggested to provide a table and describe the symbols at the start.
5. All the tables and figures need a description. I can see some tables and figures without descriptions.
6. Some literature on interval-valued t-spherical fuzzy sets may also be added to signify the concept.
7. The following paper may help in the future direction
Picture fuzzy Maclaurin symmetric mean operators and their applications in solving multiattribute decision-making problems
Author Response
Referee: 4
The paper entitled "Multi-criteria decision-making method based on complex t-spherical fuzzy Aczel-Alsina aggregation operators and its application" is an interesting article. I have been through the paper, and the results produced in the paper are novel. A few suggestions are given below for the improvement of the paper.
Comment 1: Please discuss the significance of complex t-spherical fuzzy sets in the abstract.
Reply: Abstract has been revised accordingly.
Comment 2: The introduction should add more recent and relevant literature on T-spherical fuzzy sets and Aczel Alsina aggregation operators.
Reply: Thank you for this valuable suggestion. The required change has been done.
Comment 3: I can see the author referred to [20] in lines 4th and 5th lines of page 3. Here the most suitable reference is [50] here at this place.
Reply: We have replaced Reference [20] by [50] as per your suggestion. Thanks.
Comment 4: The author is suggested to provide a table and describe the symbols at the start.
Reply: We totally agree with your valuable suggestion. But there are already more than 5 tables in the article. Therefore, we have mentioned the symbols/abbreviations just in the text.
Comment 5: All the tables and figures need a description. I can see some tables and figures without descriptions.
Reply: We have carefully checked the description/captions of all the tables and figures.
Comment 6: Some literature on interval-valued t-spherical fuzzy sets may also be added to signify the concept.
Reply: Required is done.
Comment 7: The following paper may help in the future direction
Picture fuzzy Maclaurin symmetric mean operators and their applications in solving multiattribute decision-making problems.
Reply: The suggested Reference has been added for comparison and review purposes.
Round 2
Reviewer 1 Report
The article has been revised based on the comments. It is now suitable to publish by the journal.
Reviewer 2 Report
Dear Authors,
After analyzing the revised manuscript, I find that my concerns reported in major revisions have been properly addressed. However, in the final version of the manuscript, the authors should include the clarifications contained in Responses to my comments 12 and 14. I recommend acceptance of the manuscript with mentioned corrections made.
