Review Reports

Round 1

Reviewer 1 Report

Some of the words are overlapping with the other which should be modified carefully. There are no examples in the text. It will be good to illustrate the new introduced concepts by examples.

Author Response

Dear reviewers,

Thank you very much for sending me the reviewer's comments of the paper (ID: axioms-2033672).

According to your kindly suggestions and comments, we have a new manuscript for the revised paper.
The following are revised report for the reviewers comments.
1. We have checked and correct the English errors as reviewer's suggestions, and given a substantial proofreading to eliminate those mistakes.
2. We focused on the existence of theoretical solution, so that we didn't have a suitable example in this paper.
 

The enclosed file is our new manuscript for the revised paper.

Author Response File: Author Response.pdf

Reviewer 2 Report

Please see the attached file

Comments for author File: Comments.pdf

Author Response

Dear reviewers,

Thank you very much for sending me the reviewer's comments of the paper (ID: axioms-2033672).

According to your kindly suggestions and comments, we have a new manuscript for the revised paper. 

The enclosed file is our cover letter and new manuscript  for the revised paper.

Author Response File: Author Response.pdf

Reviewer 3 Report

Report on "Second-ordered parametric duality for the multi-objective programming problem in complex space" by Hsu and Huang

 

 

In this paper, the author studied a second-ordered parametric dual model of a complex multi-objective programming problem (P) . Next, they also studied the dual problem (D) with respect to the problem (P) and prove their duality theorems under suitable conditions. Indeed, the main results in this paper are Theorem 10 (weak duality theorem), Theorem 11(strongly duality theorem), Theorem 12 (strictly converse duality theorem). From these results, we know the author gave the necessary and sufficient optimality conditions of (P), establish the second-ordered parameter dual model (D) with respect to problem (P), and discuss their duality theorems. These results are important and the proof of these results are correct. Hence, I will recommend this paper to be published.

Author Response

Dear reviewers,

Thank you very much for sending me the reviewer's comments of the paper (ID: axioms-2033672).

According to your kindly suggestions and comments, we have a new manuscript for the revised paper. 
We have checked and correct the English errors as reviewer's suggestions, and given a substantial proofreading to eliminate those mistakes. 

The enclosed file is our new manuscript for the revised paper.

Author Response File: Author Response.pdf

Reviewer 4 Report

Authors presented and introduced sufficient optimality conditions of (P), establish the second-ordered parameter dual model (D) with respect to problem (P), and discuss their duality theorems. This is multi objective optimization that is discussed in this paper. It seems that this paper might attract reader attention. But I think need to explore the subject as presented in this paper in terms of 

Add some real time examples that prove this introduced second ordered parameter dual model. It is mandatory to provide reasonable answer. 

If authors failed to provide any example or reasonable answer that proved this study so it affects on my decision. 

Author Response

Dear reviewers,

Thank you very much for sending me the reviewer's comments of the paper (ID: axioms-2033672).

According to your kindly suggestions and comments, we have a new manuscript for the revised paper.
The following are revised report for the reviewers comments.
1. We have checked and correct the English errors as reviewer's suggestions, and given a substantial proofreading to eliminate those mistakes.
2. We focused on the existence of theoretical solution, so that we didn't have a suitable example in this paper.
 

The enclosed file is our new manuscript for the revised paper.

Author Response File: Author Response.pdf

Round 2

Reviewer 4 Report

The manuscript accepted is in its present form.

Author Response

We have changed the statement in abstract as suggested. The authors would like to emphasis the related topics of the paper in the introduction. Some of the passive voice in the introduction are aimed on this purpose as most of the others do. Most of the main sections of the paper are active voice as the editor suggested. The modified sentences have been marked in red and the novelty of this work has been mentioned and highlighting in the last paragraph in the introduction as attachment.
The zip folder includes the tex-file, PDF, and PDF with highlighting.
the