An Algorithm for Producing Fuzzy Negations via Conical Sections
Round 1
Reviewer 1 Report
The presentation of the production of fuzzy negations from conic sections and their use for deducing conclusions through implications which are being created from these negations, is -in my opinion- of great interest.
This is a well-written and well-structured text, which could work as a tool for the derivation of new data in this subject, from researchers in the field.
A very positive point in this article is that, with the appropriate choice of theorems and their logical connection, and with quite simple calculations we get an original and simple (simple in a good sense!) idea for an algorithmic production of fuzzy sets.
I would only like to mention two misprints: 77-81 lines; no need to write f(x,y) and in line 183 the typo: istobefound.
Having written the above, I believe that this paper deserves publication in Algorithms.
Author Response
We have carefully considered and we have also taken in to account all the suggestions have made by the referees. Namely, we have corrected the typos, we have increased the abstract and we have presented the necessary elements in the introduction and in the conclusions, according to the referress' suggestions.
Please find the revisions made line-by-line.
We would like to thank the Editorial Office and the referees for the cooperation.
Best Regards
Basil Papadopoulos
Line 4 Typos errors (have corrected)
Line 11 We have revised the abstract following the guidelines.
Line40 We added information in the introduction by clarifying our new results, while in the end of the introduction we emphasized our motivation.
Lines 115-220 We corrected the numbering of the equations.
Lines 221-233 We enhanced our discussion by presenting an example of a family of implications through new negations which have been discussed in the present study.
Line 234 Finally, we have revised the Conclusions
Lines 261-266 New articles have been added
Reviewer 2 Report
My comments are:
1. The abstract should stand on its own and clearly reveal important points to the readers. A more detailed discussion regarding the major contribution with regard to the existing works should be given to highlight the motivation of this work.
2. Similar studies should be implied in the introduction with their differences of the present study.
3. The introduction of this paper should be increased.
4. It is better for the authors to describe how to organize the paper at the end of the introduction part.
5. Clarify what is the paper contribution and what parts of the paper are original.
6. Typos and grammar errors should be eliminated in the work. Please check the whole paper carefully.
7. Review Equations numbering, some equations have been missed numbers.
8. Conclusions convey little information. Future research directions should be provided.
9. More up-to-date studies should be added.
Comments for author File: 
Comments.pdf
Author Response
We have carefully considered and we have also taken in to account all the suggestions have made by the referees. Namely, we have corrected the typos, we have increased the abstract and we have presented the necessary elements in the introduction and in the conclusions, according to the referress' suggestions.
Please find the revisions made line-by-line.
We would like to thank the Editorial Office and the referees for the cooperation.
Best Regards
Basil Papadopoulos
Line 4 Typos errors (have corrected)
Line 11 We have revised the abstract following the guidelines.
Line40 We added information in the introduction by clarifying our new results, while in the end of the introduction we emphasized our motivation.
Lines 115-220 We corrected the numbering of the equations.
Lines 221-233 We enhanced our discussion by presenting an example of a family of implications through new negations which have been discussed in the present study.
Line 234 Finally, we have revised the Conclusions
Lines 261-266 New articles have been added
Round 2
Reviewer 2 Report
Thanks to the authors for considering the comments carefully. After examining the revised manuscript, I come to the point that this manuscript has reached to the standard of this journal. Thus, I recommend it for acceptance.
