Innovative Methods of Constructing Strict and Strong Fuzzy Negations, Fuzzy Implications and New Classes of Copulas
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsFuzzy negations are an active and evolving field and are essential in various fields and becoming popular. This paper discusses construction methods for fuzzy negations. The following are my comments/suggestions.
- The abstract needs to be rewritten. It is not formatted in the standard style. For example, usage of the phrases such as “We present one more some examples” at line no.23 detracts from the formal tone expected in research writing. The word "we" is used excessively throughout the paper. The paper should be written in the third person to enhance readability for the audience. It is recommended to thoroughly check the entire paper to ensure it is readable and properly formatted.
- The literature review is not adequate. Many references are old. It's recommended to expand the reference list to include a wider range of sources, while also prioritizing recent publications to ensure the work reflects the most up-to-date research. Besides, some of the references are not cited in the text. Please ensure that all references are cited.
- Equations are not cited in the text; it is important to cite and refer to the equations within the text. Same equation numbers are used multiple times for different equations which makes it hard to understand the work. Please check throughout the paper for this kind of issue.
- Please check the lines from 183 to 197. It's important to proofread the manuscript multiple times before submitting it.
- The discussion section should be elaborated with additional explanations to provide a clearer understanding to the reader to ensure that the significance of the findings is conveyed.
- The conclusion section should be rewritten. Summarize the key findings by highlighting their significance. Discuss the implications, explaining how your findings contribute to the field. Also, discuss the limitations and suggest areas for future research.
- The language throughout the paper must be strongly polished. The text is unclear in several parts.
Moderate editing of the English language is required.
Author Response
First comment : The abstract needs to be rewritten. It is not formatted in the standard style. For example, usage of the phrases such as “We present one more some examples” at line no.23 detracts from the formal tone expected in research writing. The word "we" is used excessively throughout the paper. The paper should be written in the third person to enhance readability for the audience. It is recommended to thoroughly check the entire paper to ensure it is readable and properly formatted.
Response 1 : the summary has been rewritten , it has been moved to the third person singular
Second comment : The literature review is not adequate. Many references are old. It's recommended to expand the reference list to include a wider range of sources, while also prioritizing recent publications to ensure the work reflects the most up-to-date research. Besides, some of the references are not cited in the text. Please ensure that all references are cited.
Response 2: the bibliography has been updated with very recent articles which have been not presented for reasons of academic ethics . also each book , article or publication has been cited in the text .
Third comment : Equations are not cited in the text; it is important to cite and refer to the equations within the text. Same equation numbers are used multiple times for different equations which makes it hard to understand the work. Please check throughout the paper for this kind of issue.
Response 3: all the equations used in definitions , theorems , propositions or remarks are cited on the article .
Forth comment : Please check the lines from 183 to 197. It's important to proofread the manuscript multiple times before submitting it.
Response 4: taken into account and explanations added in section 3 : methods and materials.
Fifth comment : The discussion section should be elaborated with additional explanations to provide a clearer understanding to the reader to ensure that the significance of the findings is conveyed.
Response 5: the discussion section has been enriched and various categories of applications of the above structures are presented .
Sixth comment : The conclusion section should be rewritten. Summarize the key findings by highlighting their significance. Discuss the implications, explaining how your findings contribute to the field. Also, discuss the limitations and suggest areas for future research.
Response 6 : the conclusion section has been rewritten and enriched . the discussions have been included in the discussions section.
Seventh comment : The language throughout the paper must be strongly polished. The text is unclear in several parts.
Response 7 : has been examined and the necessary corrections have been made.
Thank you very much for your comments and corrections.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments and Suggestions for AuthorsFollowing are the further comments/Suggestions to improve the manuscript for effective readability and interest to the readers
1. Revise the abstract as it looks very lengthy (Hint: Abstract should contain the area, problem statement, and proposed methods with the usage of tools).
2. Avoid the terms “I, We” throughout the manuscript.
3. What is the main question addressed by the research?
4. Authors used so many variables which are not defined in the manuscript check once.
5. Authors used a total of 20 references which are not reflected anywhere in the manuscript.
6. It is observed that the authors have not focused much attention on organizing the contents of the manuscript; similarly, the introduction is also poor and also informed to include more recent literature works in section 2 along with present works.
7. Results section is very poor.
8. All figure captions are to be revised.
9. Does the author consider the topic original or relevant in the field? Does it address a specific gap in the field?
10. What specific improvements should the authors consider regarding the methodology? What further controls should be considered?
11. Check the manuscript for typos and grammar
Author Response
Comment 1 : Revise the abstract as it looks very lengthy
Response 1 : The abstract haw been totally revised
Comment 2 : Avoid the terms “I, We” throughout the manuscript.
Response 2 : the language in the text has been revised and corrected .
Comment 3: What is the main question addressed by the research?
Response 3 : the introduction sector has been enriched and the questions addressed by the research are imprinted there.
Comment 4 : Authors used so many variables which are not defined in the manuscript check once.
Response 4 : every effort has been made to bring the article into line with this observation.
Comment 5 : Authors used a total of 20 references which are not reflected anywhere in the manuscript.
Response 5 : : the bibliography has been updated with very recent articles which have been not presented for reasons of academic ethics . Also each book , article or publication has been cited in the text .
Comment 6 : It is observed that the authors have not focused much attention on organizing the contents of the manuscript; similarly, the introduction is also poor and also informed to include more recent literature works in section 2 along with present works.
Response 6 : The instroduction sector has been revised and all the literature too. Ιn the literature you will find very recent research by colleagues with whom there is collaboration and the reference was avoided for reasons of academic ethics ( e.g. 24. St. Giakoumakis; B. Papadopoulos “Novel transformation of unimodal (a)symmetric possibility distributions into probability distributions” Fuzzy Sets Syst. 476: 108790 (2024) )
Comment 7 : Results section is very poor.
Response 7 : : the discussion section has been enriched and various categories of applications of the above structures are presented .
Comment 8: All figure captions are to be revised.
Response 8 : all the photos have been thoroughly reviewed despite the fact that the other two evaluators consider them to be very good.
Comment 9 : Does the author consider the topic original or relevant in the field? Does it address a specific gap in the field?
Response 9 : this paper provides solutions in the areas of fuzzy negation constructions , implication and copulas and is a continuation and extension of work done by colleagues in our collaboration ( e.g. St. Giakoumakis; B. Papadopoulos “Novel transformation of unimodal (a)symmetric possibility distributions into probability distributions” Fuzzy Sets Syst. 476: 108790 (2024), M. Rapti, B. Papadopoulos « A Method of Generating Fuzzy Implications from n Increasing Functions and n+1 Nega-tions» Mathematics 2020, 8(6), 886; http://doi.org/10.3390/math8060886, 24. St. Giakoumakis; B. Papadopoulos “Novel transformation of unimodal (a)symmetric possibility distributions into probability distributions” Fuzzy Sets Syst. 476: 108790 (2024) )
Comment 10 : What specific improvements should the authors consider regarding the methodology? What further controls should be considered?
Response 10 : there has been a comprehensive review of the methodology which is considered very good by the other evaluators.
Comment 11 : Check the manuscript for typos and grammar
Response 11 : a detailed check has been carried out
Thank you very much for your comments and corrections
Author Response File: Author Response.docx
Reviewer 3 Report
Comments and Suggestions for Authors
The manuscript titled "Innovative methods of constructing strict and strong fuzzy negations, fuzzy implications and new classes of copulas" is well-conducted and contributes significantly to the field of fuzzy logic, particularly in the construction of new fuzzy negations, implications, and copulas.
However, I have a few suggestions and minor corrections to improve the overall quality and comprehensiveness of the paper:
1. The methodology section is robust, and the proofs provided for the new theorems are thorough. Nonetheless, I recommend a clearer distinction between the different classes of fuzzy negations and implications to enhance readability.
2. Although the results of this paper can achieve the expected effect, in the revised version, adding some descriptions about fuzzy research, such as "Control synthesis for discrete-time T-S fuzzy systems based on membership function-dependent H∞ performance" and "Finite-Time Membership Function-Dependent H∞ Control for T-S Fuzzy Systems via a Dynamic Memory Event-Triggered Mechanism" will further enrich the research background of this paper.
3. There are a few areas where the clarity of the presentation can be improved. For instance, the definitions of the mathematical terms and theorems could be more explicitly connected to the examples provided later in the paper. Additionally, consider revising some of the more complex equations to ensure they are easily understandable by a broader audience.
4. The figures and tables included are appropriate and aid in the understanding of the text. Ensure that all figures and tables are referenced correctly in the text and that their captions are descriptive enough to be understood independently of the main text.
5. There are minor typographical errors throughout the manuscript. A thorough proofreading would help in eliminating these errors and improving the overall readability of the paper.
I appreciate the effort and dedication that went into this research, and I believe that with these revisions, your manuscript will be a valuable addition to the existing literature on fuzzy logic and control systems.
Thank you for considering these suggestions. I look forward to seeing the revised version of your manuscript.
There are minor typographical errors throughout the manuscript. A thorough proofreading would help in eliminating these errors and improving the overall readability of the paper.
Author Response
Comment 1 : The methodology section is robust, and the proofs provided for the new theorems are thorough. Nonetheless, I recommend a clearer distinction between the different classes of fuzzy negations and implications to enhance readability.
Response 1 : thanks for the comments . every effort has been made to recheck the distinction between negations and inferences . it is clarified after the revision in both section 2 and section 3 which proofs relate to negations and which to inferences .
Comment 2 : Although the results of this paper can achieve the expected effect, in the revised version, adding some descriptions about fuzzy research, such as "Control synthesis for discrete-time T-S fuzzy systems based on membership function-dependent H∞ performance" and "Finite-Time Membership Function-Dependent H∞ Control for T-S Fuzzy Systems via a Dynamic Memory Event-Triggered Mechanism" will further enrich the research background of this paper.
Response 2 : thank you for the suggestion . the areas you suggest have been examined in detail and have been extensively referenced both in the discussion section and in the bibliography of the article.
Comment 3: There are a few areas where the clarity of the presentation can be improved. For instance, the definitions of the mathematical terms and theorems could be more explicitly connected to the examples provided later in the paper. Additionally, consider revising some of the more complex equations to ensure they are easily understandable by a broader audience.
Response 3 : concerning this fact , for this very reason all the functions , theorems , propositions and remarks have been numbered .
Comment 4 : The figures and tables included are appropriate and aid in the understanding of the text. Ensure that all figures and tables are referenced correctly in the text and that their captions are descriptive enough to be understood independently of the main text.
Response 4 : the photos have been revised and some descriptive explanations have been given.
Comment 5 : There are minor typographical errors throughout the manuscript. A thorough proofreading would help in eliminating these errors and improving the overall readability of the paper.
Response 5 : there has been a major revision of the texts of the article as you will see .there have been a large number of corrections .
Thank you very much for your comments and corrections
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Comments and Suggestions for Authors
Most of the revisions are satisfactory. Further, I could see that the figure captions are missed in the revised version. Please crosscheck and add the captions for all figures.
Author Response
First comment : I could see that the figure captions are missed in the revised version. Please crosscheck and add the captions for all figures.
Response 1 : All pictures and tables have captions on them. Besides that , additionally , there has been changed :
- all large equations have been placed in one form to make them easier to study.
- all non-numbered equations have a discrete bullet
- larger gaps have been created between the large equations to make them easier to read
- all equations have been written in italics to make them easier to read.
- All the above are highlighted.
The authors would like to thank you very much for your comments and remarks.
Author Response File: Author Response.docx
Reviewer 2 Report
Comments and Suggestions for Authors1. It is informed to all the authors that before uploading the revised version please ensure all the concerns raised by the reviewer are properly addressed or not, if addressed then the same thing has to be highlighted with a different color for easy identification.
2. See the following example for your understanding
where is the figure caption? the same thing can apply to the remaining figures. Captions indicate what the picture represents and what information we can get from that figure.
3. I disagree with the answer to the concern raised "What specific improvements should the authors consider regarding the methodology? What further controls should be considered?"
Author Response
First comment : It is informed to all the authors that before uploading the revised version please ensure all the concerns raised by the reviewer are properly addressed or not, if addressed then the same thing has to be highlighted with a different color for easy identification.
Response 1 : All the changes made to the manuscript have been highlighted.
Second comment : where is the figure caption? the same thing can apply to the remaining figures. Captions indicate what the picture represents and what information we can get from that figure.
Response 2: All pictures and tables have captions on them. Highlighted.
Third comment : I disagree with the answer to the concern raised "What specific improvements should the authors consider regarding the methodology? What further controls should be considered?"
Response 3: Additionally , there has been changed :
- all large equations have been placed in one form to make them easier to study.
- all non-numbered equations have a discrete bullet
- larger gaps have been created between the large equations to make them easier to read
- all equations have been written in italics to make them easier to read.
All the above are highlighted.
The authors would like to thank you very much for your comments and remarks.
Author Response File: 
Author Response.pdf
