Optimizing Sensor-Controlled Systems with Minimal Intervention: A Fuzzy Relational Calculus Approach

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors This article describes an approach to the important applied problem
of optimizing sensor-controlled systems by solving a fuzzy system of
linear equations. The introduction describes in sufficient detail the
history of the formulation and solution of this problem. For a fuzzy
system of linear equations, the direct and inverse problems are solved.
The solution of the direct problem has polynomial complexity, and the
solution of the inverse problem has exponential complexity. It is known
that any solvable maximum−minimum fuzzy linear system of equations has a
single largest solution and one or more smallest solutions. All solutions
between the largest solution and any of the smaller solutions are also
solutions (5).   This paper describes an algorithm for finding the largest solution and
the smallest solutions. A numerical example is described in sufficient
detail. It seems to me that such an algorithm in itself is an important
computational result. Judging by the list of publications presented in
the article, this result required long-term work from the authors (about
fifteen years). This circumstance allows me to consider this paper for
possible publication in the journal Computation.  

 

However, the very high computational complexity of the algorithm proposed
by the author is confusing. The question arises whether it is possible to
somehow reduce the complexity of the algorithm. Are there any circumstances
that reduce the complexity of solving the problem? And then one example seems
insufficient for such a publication. Is it possible to find any additional
example other than the one discussed in the article? The relatively small
number of links before 2011 and the lack of recent links are confusing.
Therefore, I recommend major revision for further processing of this article.

Author Response

Dear reviewer,

Thank you so much for the review, and the highly related and valuable comments and suggestions. In a short I'll upload a revised version hopefully addressing all the comments:
1. The very high computational complexity - In the new revision (lines 153-165) It is now clearly stated, what optimizations are done in the used software to address the complexity issue, alongside with a citation to be followed for further details.
2. One example seems insufficient - I fully agree. However, in the current state of the research - it is more or less still in its theoretical stage. This is now clearly stated (new revision lines 200-206). Nevertheless, a second example is added (new revision lines 268-277) to demonstrate the practical usability of the presented software.
3. The relatively small number of links before 2011 and the lack of recent links - more links added and referred in the article body (new revision lines 306-373, 391-395)

The text is generally edited in order to improve its background and clear out the used methods.

Thank you!

Best regards,
Zlatko

Reviewer 2 Report

Comments and Suggestions for Authors

In this paper, by using Fuzzy Linear Systems of Equations the authors considered an approach for optimizing sensor-controlled systems through minimal intervention. By achieving minimal intervention, the system can be ensured to adjust effectively, economically optimal and non-intrusive. Finally, some numerical examples were given. Some special comments are presented as follows.

1) The research background of this paper should be improved in the introduction part.

2) The authors should clarified the motivations and contributions of this paper. 

3) Some remarks should be added to show the advantages of this paper comparing this paper with the results of the related existing references.

4) Do you confirm the covergence of the algorithms mentioned in this paper? 

5) Do the intial values effact the  covergence of the algorithms?

Author Response

Dear reviewer,

Thank you so much for the review, and the highly related and valuable comments and suggestions. In a short I'll upload a revised version hopefully addressing all the comments:

1) Improved, with some more background information and references
2) Hopefully clarified (new revision lines 49-56)
3) Hopefully addressed through the text (lines 36-38, 49-56, 153-165, 268-277)
4) I hope that the newly added and cited references (lines 306-373, 391-395) confirm that. I personally also do, having in mind that the current state of the research is still more or less theoretical.
5) Short answer is "no". As stated now (line 36-38) FLSEs are great way to deal with imprecisions and uncertainty. Also the examples in the article are random anyway.

The text is generally edited in order to improve its background and clear out the used methods.

Thank you!

Best regards,
Zlatko

Reviewer 3 Report

Comments and Suggestions for Authors

1.The manuscript should explicitly state the novel contributions of the proposed approach compared to existing methods in the field. Highlight how the use of Fuzzy Linear Systems of Equations (FLSE) and fuzzy relational calculus sets this work apart and advances the state-of-the-art in optimizing sensor-controlled systems with minimal intervention.

 

2. Provide more details on the implementation of the fuzzy inference system as part of the fuzzy rule-based expert knowledge base. Explain the selection criteria for fuzzy if-then rules and how they are derived from the expert knowledge module.

 

3. Discuss practical challenges or limitations that may arise during the implementation of the proposed approach in real-world sensor-controlled systems. For example, consider issues related to sensor accuracy, data fusion from multiple sensors, and computational complexity in handling large-scale systems.

 

4. Enhance the manuscript by including case studies or simulated examples to demonstrate the application of the proposed approach in different scenarios. Show how the method performs in terms of achieving minimal intervention while optimizing system performance.

 

5. Conduct robustness analysis to evaluate the performance of the approach under varying conditions or uncertainties in sensor data. Additionally, perform sensitivity analysis to assess the impact of small changes in input parameters on the system's behavior and intervention levels.

 

6.  If possible, include a comparative analysis with other optimization techniques or control strategies to showcase the strengths and limitations of the proposed FLSE-based approach. This can help readers understand the relative advantages of adopting this methodology.

 

7. Conclude the manuscript with a section on future research directions and potential extensions of the proposed approach. Discuss avenues for enhancing the algorithm's capabilities, such as incorporating machine learning techniques for adaptive control or extending the method to dynamic systems.

 

8. Review the manuscript for clarity, coherence, and logical flow of ideas. Ensure that each section builds upon the previous ones seamlessly and that technical terms are defined or explained where necessary for readers who may be less familiar with fuzzy logic or FLSE.

 

Would you like me to add any specific comments or suggestions based on the manuscript's content?

Comments on the Quality of English Language

NaN

Author Response

Dear reviewer,

Thank you so much for the review, and the highly related and valuable comments and suggestions. In a short I'll upload a revised version generally edited in order to improve its background and clear out the used methods.
- Lines 49-66, partially answering comments 1, 4, 6
- Lines 153-165, partially answering comments 1, 5, 6
- Lines 268-277, partially answering comments 1, 5
- Lines 290-296, partially answering comments 2, 3. 7
- Lines 306-373, 391-395 (alongside with the text that refers it), answering comment 4

Please excuse me - I'm not fully answering some of the comments in this revision:
2. I added more refences where such techniques are considered ([12-16]), also in [11] there is one developed by me.
3., and 5. It is now clearly stated, that at this stage stated the research is more or less still theoretical. However, FLSEs are a great way to deal with imprecisions and uncertainty. 
8. The text is generally edited in order to improve its background and clear out the used methods.

Finally - Of course I'll be happy to have any specific comments or suggestions based on the manuscript's content. While my background is relatively good in FLSE, the sensor controlled systems are more or less new area for me. 

Thank you!

Best regards,
Zlatko

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I am satisfied with the author's answers and recommend the article for publication in present form.

Reviewer 2 Report

Comments and Suggestions for Authors

The revised version is ok. Therefore, I recommend it accepted.

Reviewer 3 Report

Comments and Suggestions for Authors

No further comments

Comments on the Quality of English Language

No further comments