Realistic Optimal Tolerant Solution of the Quadratic Interval Equation and Determining the Optimal Control Decision on the Example of Plant Fertilization
Round 1
Reviewer 1 Report
The manuscript of applsci-1910192 entitled “Realistic optimal tolerant solution of the quadratic interval equation and determining the optimal control decision on the example of plant fertilization”. The manuscript in its current form lacked a strong justification of the novelty of the study. The research gap was not stated clearly as well. Moreover, the manuscript in its current form lacked a comprehensive analysis which is essential for publication. Unfortunately, I am against the publication of this paper in this journal.
Other comments for consideration for the next submission in another journal:
1. Define acronyms at first mention. Also, the authors should ensure that the acronyms are not repeatedly defined in the whole manuscript.
2. The abstract is poorly written. In its current form, the abstract is too general and vague. Moreover, the key values from the results are insufficient to delineate the whole picture of the contribution and possible application of this study. It is suggested to add the background with a few objectives, key values from the results, and possible applications of this study, and highlight the novelty of this work clearly.
3. Proofread the whole manuscript to minimize text or grammatical errors.
4. Review all in-text citations. The authors clearly did not use the journal’s format in the author’s guide. Put a space before all the in-text citations.
5. In the last paragraph of the introduction section, please underscore the research gap and novelty of the study.
6. Please underscore the scientific value-added of your paper in your abstract and introduction.
7. There should be no lumping of references. This can indicate a bad literature review. Please separate the citation in its own sentence to highlight each work properly.
8. The obtained values in the results are just stated in the text without explaining them. Explain comprehensively the rationale of the results. Also, this section severely lacks a comprehensive discussion. The paper looks like a class exercise activity which is not suitable for publication.
9. Update your references accordingly. Cite references in the last 3 years for future projection discussions.
10. Upgrade the quality of all your figures. Make the font style and size consistent.
11. Please make sure your conclusions section underscores the scientific value-added of your paper. The authors are advised to write the conclusions in a comprehensive way and should contain key values, suitability of the applied method, the major findings, contributions, and possible future outcomes.
Author Response
Responses to the comments can be found in the attached file.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Thank you for inviting me as a reviewer for the paper titled Realistic optimal tolerant solution of the quadratic interval equation and determining the optimal control decision on the example of plant fertilization. First of all, the aims and scope of the paper match those of Applied Sciences. The manuscript is very interesting and well organized. The literature analysis is very well done. A minor complaint is related to the absence of more papers from the period 2020-2022. The methodology is well described and applied. Theoretical and mathematical explanations are accompanied by examples. I congratulate the authors on a very high-quality paper.
Author Response
Responses to the comments can be found in the attached file.
Author Response File: Author Response.pdf
Reviewer 3 Report
The following revisions are advisable to the authors; these are listed given below:
1: Provide software commends of this paper as an annexure after the reference list so that any researcher can verify the results. I also want to see the analysis part. Provide it according to your analysis ordering of this paper.
2: The literature review is brief. Some of the included papers could be briefly described. Also, a general overview of the topic could be included. List your work's novelty and how it differs from previously published work.
5: The research gap, novelty, applications, and limitations of the study must be highlighted in the revised version of the paper.
6: Some papers can be reviewed and added to the literature. This journal itself published some papers so add some more related papers. For Instant, you can see some of the papers given below and many others you can search and add for quality improvement and justify the applications of your proposed work.
The LR-Type Fuzzy Multi-Objective Vendor Selection Problem in Supply Chain Management.Mathematics, 8(9), 1621. https://doi.org/10.3390/math8091621.
A Theoretical Framework for Optimality Conditions of Nonlinear Type-2 Interval-Valued Unconstrained and Constrained Optimization Problems Using Type-2 Interval Order Relations" Mathematics 9(8): 908. https://doi.org/10.3390/math9080908
7: The work applications are poorly defined; it is advisable to add them correctly in the revision and highlight the same.
9: Contributions are a little bit unclear and confusing in several places. This should be made clear from the very beginning of the paper till its end.
Author Response
Responses to the comments can be found in the attached file.
Author Response File: Author Response.pdf
Reviewer 4 Report
Review Report
Journal: Applied Sciences
Manuscript ID: applsci-1910192
Title of the Manuscript: Realistic optimal tolerant solution of the quadratic interval equation and determining the optimal control decision on the example of plant fertilization
Authors: Andrzej Piegat , Marcin Pluciński
The authors develop a method for solving quadratic interval equations using the multidimensional interval arithmetic and robustness of the solution to a set of possible states of a system resulting from the uncertainty of its mathematical model. The provided solutions combine the features of tolerant and united solutions. The authors present a numerical example of the method to optimize plant fertilization on the example of sugar beets.
Comments and suggestions:
· References are not uniformly written. Check them. For examples:
o Buckley, J.; Qu, Y. Solving linear and quadratic fuzzy equations. Fuzzy sets and systems 1990, 38, 43–59.
o Buckley, J.; Qu, Y. Solving systems of linear fuzzy equations. Fuzzy sets and systems 1991, 43, 33–43.
o Buckley, J. Solving fuzzy equations. Fuzzy sets and systems 1992, 50, 1–14.
Comments for author File: Comments.pdf
Author Response
Responses to the comments can be found in the attached file.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Unfortunately, the revised version of the manuscript could still not warrant publication due to insufficient justification of the novelty.
Author Response
Responses to the comments can be found in the attached file.
Author Response File: Author Response.pdf
Reviewer 3 Report
The authors have revised the paper carefully and clarified all the queries efficiently. I recommend this work now for publication in this current version.
Author Response
Thank you for your positive review.
