Analysis of Interval-Valued Intuitionistic Fuzzy Aczel–Alsina Geometric Aggregation Operators and Their Application to Multiple Attribute Decision-Making
, Radko Mesiar 3,4, Vladimir Simic 5, Aiyared Iampan 6,*, Ronnason Chinram 7 and Rifaqat Ali 8Round 1
Reviewer 1 Report
See the attached file. Thanks.
Comments for author File: 
Comments.pdf
Author Response
Response to Reviewer 1 Comments
General Comments: This paper proposes some Aczel-Alsina geometric aggregation operators to deal with the multicriteria decision making problems with interval-valued intuitionistic fuzzy numbers. I make five general comments on this paper.
Response: We are thankful to the reviewer for their constructive comments on our paper, which helped to improve our research work. We hope that this revised version meets all the requirements of the respected reviewers. Also, we highly agree with the comments and suggestions made by the respected reviewer. Please consider it for publication.
Point 1: Reference 31 [T. Senapati, G. Chen, R.R. Yager, Aczel-Alsina aggregation operators and their
application to intuitionistic fuzzy multiple attribute decision making, Int. J. Intell. Syst., 37(2) (2022),
1529-1551.] presents the intuitionistic fuzzy Aczel-Alsina arithmetic aggregation operators. Moreover, each interval value of the intuitionistic fuzzy number has two components. One is the lower bound. The other is the upper bound. The computations of the interval-valued intuitionistic fuzzy Aczel-Alsina geometric aggregation operators are component wise. It follows that the contribution of this paper is marginal. The motivation of using intervalvalued intuitionistic fuzzy Aczel-Alsina geometric aggregation operators cannot been seen from this paper.
Response 1: Please see Subsection 1.1 “Motivation of the study” and 1.2 “Structure of this study”(Page 2 & 3).
Point 2: Secondly, the notation and domain of the parameter of the Aczel-Alsina t-norms and Aczel-Alsina tconorms should be clarified. The notation of the first definition of Aczel-Alsina t-norms and tconorms appearing in page 4 is φ. However, the Proposition 1 and Definition 8 appearing in page 7, the notation of Aczel-Alsina t-norms and t-conorms is ð. The proof of Theorem 1 appearing in page
8, the notation of Aczel-Alsina t-norms and tconorms is ð. The domain of the parameter of the Aczel-
Alsina t-norms and Aczel-Alsina t-conorms is [0, ∞] for the first definition of the Aczel-Alsina t-norms and t-conorms, and ð ≥ 1 for the Proposition 1, Definition 8 and Theorem 1 of the paper. Moreover, the Theorem 2 do not present the domain of the parameter of the Aczel-Alsina t-norms and tconorms.
Response 2: Thank you, sir, for pointing out our mistakes. We have revised accordingly.
Point 3: Thirdly, add some equations explaining why ?̃(̇1)1/? = ? ̃1?1 appearing in page 14 line 372 of the paper. A simple example is given in Section 5 to illustrate the proposed approach. The authors should conduct some computational experiments to analyze the properties of the proposed method.
Response 3: Please see Section 8 (Sensitivity analysis (SA) of criteria weights) (Page 17).
Point 4: Some abbreviations, some notation errors and some mistakes appear in the paper.
Response 4: We have revised accordingly. Please see Table 1 (List of abbreviations) (Page 1).
Author Response File: 
Author Response.docx
Reviewer 2 Report
In the paper the authors introduce several IVIFN operations, such as the Aczel-Alsina sum, the Aczel-Alsina product, and the Aczel-Alsina scalar multiplication. And then start creating IVIF aggregation operators, such as the IVIF Aczel-Alsina weighted geometric operator, the IVIF Aczel-Alsina ordered weighted geometric operator, and the IVIF Aczel-Alsina hybrid geometric operator, among others. For each of the operators, they put up a set of characteristics. They present a MADM approach that relies on the IVIF aggregation operators that have been developed.
The subject of the paper is interesting. I think the paper can be published after considering the following comments:
The abstract of the paper is long. I suggest a shorter abstract.
The paper needs an English punctuation check, for example "." in line 205 etc.
There are many theorems without proof. I suggest they cite their proofs in the text.
Is there any reason that the authors use particular letters in the paper instead of simple English letters?
Author Response
Response to Reviewer 2 Comments
General Comments: In the paper the authors introduce several IVIFN operations, such as the Aczel-Alsina sum, the Aczel-Alsina product, and the Aczel-Alsina scalar multiplication. And then start creating IVIF aggregation operators, such as the IVIF Aczel-Alsina weighted geometric operator, the IVIF Aczel-Alsina ordered weighted geometric operator, and the IVIF Aczel-Alsina hybrid geometric operator, among others. For each of the operators, they put up a set of characteristics. They present a MADM approach that relies on the IVIF aggregation operators that have been developed.
The subject of the paper is interesting. I think the paper can be published after considering the following comments:
Response: Thank you, Sir, for your recommendation “The subject of the paper is interesting. I think the paper can be published after considering the following comments ". We are thankful to the reviewer for their constructive comments on our paper, which helped to improve our research work. We hope that this revised version meets all the requirements of the respected reviewers. Also, we highly agree with the comments and suggestions made by the respected reviewer. Please consider it for publication.
Point 1: The abstract of the paper is long. I suggest a shorter abstract.
Response 1: As per your suggestions, we have revised the Abstract.
Point 2: The paper needs an English punctuation check, for example "." in line 205 etc.
Response 2: We have improved the language with our best efforts and removed all errors.
Point 3: There are many theorems without proof. I suggest they cite their proofs in the text.
Response 3: We have revised accordingly.
Point 4: Is there any reason that the authors use particular letters in the paper instead of simple English letters?
Response 4: Thank you, Sir, for your detailed observation. Sometimes we have used different words to reduce the plagiarism of the paper.
Author Response File: Author Response.docx
Reviewer 3 Report
This paper deals with an analysis of interval-valued intuitionistic fuzzy Aczel-Alsina geometric aggregation operators and their application to multiple attribute decision-making. I would like to point out or comment following as:
- In introduction, description of object in this paper is very ambiguous.
- In introduction, the description of previous work should add their advantage and disadvantage.
- What is the differentiation compared to previous works? What is novelty? It is not clear. I cannot find the novelty. Please add it.
- Please add following reference if they are related
Fuzzy Parameterized Bipolar Fuzzy Soft Expert Set and Its Application in Decision Making
Muhammad Ibrar, Asghar Khan, Sajjad Khan, and Fatima Abbas
International Journal of Fuzzy Logic and Intelligent Systems 2019; 19(4): 234-241https://doi.org/10.5391/IJFIS.2019.19.4.234
Group Decision Making Using Intuitionistic Hesitant Fuzzy Sets
Ismat Beg and Tabasam Rashid
International Journal of Fuzzy Logic and Intelligent Systems 2014; 14(3): 181-187https://doi.org/10.5391/IJFIS.2014.14.3.181
Author Response
Response to Reviewer 3 Comments
General Comments: This paper deals with an analysis of interval-valued intuitionistic fuzzy Aczel-Alsina geometric aggregation operators and their application to multiple attribute decision-making. I would like to point out or comment following as:
Response: We are thankful to the reviewer for their constructive comments on our paper, which helped to improve our research work. We hope that this revised version meets all the requirements of the respected reviewers. Also, we highly agree with the comments and suggestions made by the respected reviewer. Please consider it for publication.
Point 1: In introduction, description of object in this paper is very ambiguous.
Response 1: Please see Subsection 1.1 “Motivation of the study” and 1.2 “Structure of this study”(Page 2 & 3).
Point 2: The description of previous work should add their advantage and disadvantage.
Response 2: Please see Section 9 (Comparison Study) (Page 17).
Point 3: What is the differentiation compared to previous works? What is novelty? It is not clear. I cannot find the novelty. Please add it.
Response 3: Previous papers do not discuss sensitivity analysis of criteria weights. In this paper, we discussed the sensitivity analysis of criteria weights. Please see Section 8 “Sensitivity analysis of criteria weights” (Page 17).
Point 4: Please add following reference if they are related
Fuzzy Parameterized Bipolar Fuzzy Soft Expert Set and Its Application in Decision Making, Muhammad Ibrar, Asghar Khan, Sajjad Khan, and Fatima Abbas, International Journal of Fuzzy Logic and Intelligent Systems 2019; 19(4): 234-241https://doi.org/10.5391/IJFIS.2019.19.4.234
Group Decision Making Using Intuitionistic Hesitant Fuzzy Sets, Ismat Beg and Tabasam Rashid
International Journal of Fuzzy Logic and Intelligent Systems 2014; 14(3): 181-187https://doi.org/10.5391/IJFIS.2014.14.3.181
Response 4: As per your suggestion, we have added the relevant papers to our reference list.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
See the attached file. Thanks.
Comments for author File: Comments.pdf
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 2 Report
Now, after this modification they did on the paper, it can be published.
Author Response
Thank you for your recommendation "Now, after this modification they did on the paper, it can be published." We have improved the language with our best.
Reviewer 3 Report
I think this paper is well revised according to reviewer's point out. Thus I would like to decide as an 'accept"
Author Response
Thank you for your recommendation "Accept". We have improved the language with our best.
Round 3
Reviewer 1 Report
I suggest to publish this carefully revised version of the paper.
