PONE-D-24-12527On Fuzzy Henstock-Stieltjes Integral on Time Scales with respect to Bounded Variation FunctionPLOS ONE

Dear Dr. Shao,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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ACADEMIC EDITOR: 

​In this paper, the authors considered investigating the basic theory of the Henstock-Stieltjes fuzzy integral with respect to a bounded variation function on the time scale. The considered problem is interesting and the results are proven by the standard method, and the paper can be considered for publication after corrections:

1) The state of the art must be improved.

2) An extensive review of the text of the paper must be carried out. Typing errors must be eliminated, mathematical notations must be presented appropriately according to the Journal template;

3) Preliminaries about time scales should be provided in the second section;

4) Some applications of the main results must be presented;

5) The authors included many preliminaries. It would be beneficial if they provided a brief explanation of their relevance to the results;

6) Quote Definition 3.1 and others;

7) There are not enough smooth connections between results. It is recommended that authors provide a few introductory lines before stating and proving each new result;

8) If possible, could the authors include any corollaries and observations for = and T=Z?

9) The results are applicable to general time scales and therefore may be relevant to both continuous and discrete time scales. It would be beneficial to compare these results with those existing on real, discrete time scales, if possible;

10) The conclusion section is very brief. Should provide a more detailed explanation.

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Please submit your revised manuscript by Jun 09 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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We look forward to receiving your revised manuscript.

Kind regards,

Angelo Marcelo Tusset

Academic Editor

PLOS ONE

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4. Please amend either the abstract on the online submission form (via Edit Submission) or the abstract in the manuscript so that they are identical.

Additional Editor Comments:

In this paper, the authors considered investigating the basic theory of the Henstock-Stieltjes fuzzy integral with respect to a bounded variation function on the time scale. The considered problem is interesting and the results are proven by the standard method, and the paper can be considered for publication after corrections:

1) The state of the art must be improved.

2) An extensive review of the text of the paper must be carried out. Typing errors must be eliminated, mathematical notations must be presented appropriately according to the Journal template;

3) Preliminaries about time scales should be provided in the second section;

4) Some applications of the main results must be presented;

5) The authors included many preliminaries. It would be beneficial if they provided a brief explanation of their relevance to the results;

6) Quote Definition 3.1 and others;

7) There are not enough smooth connections between results. It is recommended that authors provide a few introductory lines before stating and proving each new result;

8) If possible, could the authors include any corollaries and observations for = and T=Z?

9) The results are applicable to general time scales and therefore may be relevant to both continuous and discrete time scales. It would be beneficial to compare these results with those existing on real, discrete time scales, if possible;

10) The conclusion section is very brief. Should provide a more detailed explanation.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: No

Reviewer #2: N/A

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3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: No

Reviewer #2: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: In this paper, the authors considered investigate the basic theory of fuzzy Henstock-Stieltjes Δ-integral with respect to a bounded variation function on time scale. A series of mian results about fuzzy Henstock-Stieltjes Δ-integrable function were presented. Then some examples were also given to show the effectiveness of main results. The main reuslts of this paper are interesting and their proofs seem to be correct. Some speical comments are given as follows.

1) The research background of this paper should be improved.

2) Preliminaries on time scales should be provided in the second section.

3) Some applications of the main results should be given.

Reviewer #2: The considered problem is interesting, and the results are proven with the standard method. However, the representation of the paper is not satisfactory. It requires some revision. I have some suggestions and comments. Please see the attached file.

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6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

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Attachments

Attachment

Submitted filename: Report on PLOS-ONE-D-24-12527.pdf

On Fuzzy Henstock-Stieltjes Integral on Time Scales with Respect to Bounded Variation Function

PONE-D-24-12527R1

Dear Dr. Yabin Shao,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Angelo Marcelo Tusset

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

The authors presented a fully revised version, meeting all the requested corrections and the criteria required for publication of this Journal.

After these considerations, I consider the paper accepted in its current form.

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #3: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #3: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #3: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #3: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #3: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The authors have answered my concerned questions in the revised version. Therefore, I recommend it accepted for Plos one.

Reviewer #3: The author has made the changes requested by the reviewers. The article is good enough to be published.

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7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #3: No

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