Categories of L-Fuzzy Čech Closure Spaces and L-Fuzzy Co-Topological Spaces
Round 1
Reviewer 1 Report
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Comments for author File: 
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Author Response
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Reviewer 2 Report
The reviewed work is devoted to one of the sections of theoretical mathematics - fuzzy topology. The authors consistently present their ideas related to the search for the relationship between the L-fuzzy (fuzzy) closure space and the L-fuzzy (fuzzy) topological space. At the same time, a number of interesting conclusions are obtained, which are presented in the form of various theorems and statements. The presentation of the material has a logical harmony and is based on a deep theoretical analysis. Speaking about the applied significance of the results obtained, it should be noted that, as a whole, in science it is episodic and superficial. This article, of course, will help to popularize the ideas of fuzzy topology and, possibly, expand the application of applied problems, for example, economics.
Author Response
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Reviewer 3 Report
The authors in the paper present relationships between the category of L-fuzzy co-topology, the category of L-fuzzy Cech closure spaces and the category of reflexive L-fuzzy approximation spaces. The paper is interesting. Below are my comments and recommendations.
[1] What was authors motivation to conduct this research? This is not clearly stated in the paper. The motivation should be included in the introduction section.
[2] It would be better if the authors showed the relationships also on examples.
[3] Lines 285 and 286 are the same. One of them should be removed.
[4] The conclusions section should be extended. A summary of the research presented in the paper should be added.
Author Response
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Reviewer 4 Report
>Abstract should present additional information about used methods.
>Conclusions can be obtained after analysis of results (corollary). However, proper remarks should be presented in the last part of the article.
>I know that the article is proposed for publication dedicated to group of readers qualified in this area. However, the formulas and used symbols need additional explanations.
>Some numerical examples would be interesting.
>I have noticed, in papers related to this issues, interesting applications of analyzed models. Could you propose examples of applications?
Author Response
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Reviewer 5 Report
Review for manuscript ID mathematics-810182
This manuscript requires some minor corrections.
- Positive aspects.
1.1. This study shows a very good knowledge of the fundamental elements of fuzzy spaces, fuzzy sets, rough sets etc. It is based on a clear idea and is seriously investigating it. The results are verifiable and acceptable.
1.2. As topic and value, this manuscript is adapted to journal „Mathematics”.
- Negative aspects
2.1. Neither in “Abstract” (“In between, some categorical results have been3 established.”) nor in “Conclusions” (“In particular, we obtain some interesting adjunctions between the considered categories”) the main results obtained are not specified. Our collegial request is to specify in concrete terms the results obtained.
2.2. The bibliography does not contain any reference from 2020: this is required.
2.3. The article does not follow the journal's „Mathematics — Instructions for Authors” elaboration guide for the References section: the quoting of references does not follow the instructions for authors. This inadvertence must be eradicated.
See
https://www.mdpi.com/journal/mathematics/instructions
In the text, reference numbers should be placed in square brackets [ ], and placed before the punctuation; for example [1], [1–3] or [1,3]. For embedded citations in the text with pagination, use both parentheses and brackets to indicate the reference number and page numbers; for example [5] (p. 10). or [6] (pp. 101–105).
The reference list should include the full title, as recommended by the ACS style guide. Style files for Endnote and Zotero are available.
Comments for author File: Comments.docx
Author Response
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Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
The authors have revised the paper taking into account SOME of the referees critical remarks. the revised version is certainly better then the original one. However, there are several misprints and language mistakes in the paper, especially in the Introductory part. After the authors eliminate them, the paper can be published in MATHEMATICS journal.
Author Response
We first thank the reviewers for recognizing our revised version. We are pleased that the mathematical content has been fully accepted.
We agree with Reviewer No. 1 regarding language corrections. As a result, we made a complete review of the quality of the language and rewrote the introduction. For the convenience of reviewers, we include the pdf-file “Revision", where all corrections are highlighted in blue and the previous text in red.
With the exception of some typographical corrections, the main text has not been changed.
On behalf of the authors,
Irina Perfilieva
Reviewer 3 Report
The authors answered my questions. I recommend the article for publication.
Author Response
We first thank the reviewers for recognizing our revised version. We are pleased that the mathematical content has been fully accepted.
We agree with Reviewer No. 1 regarding language corrections. As a result, we made a complete review of the quality of the language and rewrote the introduction. For the convenience of reviewers, we include the pdf-file “Revision", where all corrections are highlighted in blue and the previous text in red.
With the exception of some typographical corrections, the main text has not been changed.
On behalf of the authors,
Irina Perfilieva
