Generalized Neutrosophic Extended Triplet Group

Round 1

Reviewer 1 Report

 In this manuscript the concept off generalized neutrosophic extended triplet group is introduced and some properties are discussed.

Section 2 is called "Related works", but only definitions are given. A discussion about related researches in literature is necessary.

Example 1 is not clear enough and needs to be better structured. 

Examples related to theorems 5-13 and definitions 8-10 must be added.

Author Response

Response to Reviewer 1 Comments

 

Dear Editors and Reviewers:

We are very grateful to you for the constructive suggestions and comments concerning our manuscript entitled “Generalized Neutrosophic Extended Triplet Group” (symmetry-449311). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. Moreover, we have made a thorough revision of the manuscript, including:

1) The English expression has been thoroughly revised, including grammar, spelling, singular and plural, tense and so on.

2) The format of the paper has been revised in detail, including changing some theorems to propositions, citations, proving environment, etc.

3) Some new references have been added and detailed revisions were made in accordance with the reviewers.

Below you will find our point-by-point responses to the comments by red fonts:

 

 

In this manuscript the concept off generalized neutrosophic extended triplet group is introduced and some properties are discussed.

 

Point 1: Section 2 is called "Related works", but only definitions are given. A discussion about related researches in literature is necessary.

Response 1:  

Thank you very much for your suggestions. We have expanded the Section 2, including:

1) The introduction of related definitions and theorems;

2) The addition of important results of NETG;

3) The relationship between current NETG and other algebraic systems.

 

Point 2: Example 1 is not clear enough and needs to be better structured.

Response 2:

We have added another example to give a more direct understanding of the meaning of the theorems. At the same time, the language expression of original Example 1 has been modified to make it easier to understand.

 

Point 3: Examples related to theorems 5-13 and definitions 8-10 must be added.

Response 3:

We have added many examples to explain and describe the definitions and theorems in this paper. These examples can make it easier to understand the contents of the definitions and theorems in the paper. Thank you very much for your suggestion. The addition of these examples has greatly promoted the quality of the paper.

 

Thanks again for your valuable comments.

 

Author Response File: Author Response.docx

Reviewer 2 Report

The authors are dealing with the neutrosophic triplet groups. In this paper, the authors define and discover new results and properties for the generalized neutrosophic extended triplet groups based on semigroup theory.

 

Ma et al. prove the equality of this group with the quasi completely regular semigroup and the equality of the weak commutative property in this group with the quasi Clifford semigroup.

 

On the other hand, the authors study the relationships of (Zn, ⊗) and neutrosophic extended triplet.

 

This manuscript is a continuation of the work of the neutrosophic triplet groups developed by coauthor Xiaohong Zhang.

 

The motivation and justification of the work are appropriate. The paper is well written in correct English. The examples included are adequate.

 

 

Now I include some typographical errors:

 

Pg. 1, line 32

For: provided in section

read: provided in section 5

 

Pg. 3, line 88

For: the the neutral

read: the neutral

 

Pg. 3, line 92

For: From Theorem 2, we have

read: From Theorem 2, we have:

For the sake of clarity, the following lines can be established in an itemize environment.

 

Pg. 4, line: 135

The following condition must be added in as a third condition: commutative generalized neutrosophic extended triplet group

 

Pg. 5, lines: 148-154

For the sake of clarity, these results can be established in an itemize environment.

 

Pg. 6, lines: 185 and 186

For: , From Definition 6 and Theorem 7,

read: , from Definition 6 and Theorem 7,

 

Pg. 7, line: 196

For: following hold.

read: following hold:

 

Pg. 7, line: 198

For: respectively. so

read: respectively. So

 

Pg. 8, line: 202

For: GNETG, From Definition 6, for

read: GNETG, from Definition 6, for

 

Pg. 9, line: 212

It could be clearer:

“For any a, b \in N, the following conditions are satisfied:”

Instead of:

“Then a, b \in N:”

 

Pg. 10, line: 220

For: a quasi Clifford semigroup. then there are

read: a quasi Clifford semigroup, then there are

 

Pg. 10, line: 221

For: Applying Definition 10, Being

read: Applying Definition 10, being 

 

Author Response

Dear Editors and Reviewers:

We are very grateful to you for the constructive suggestions and comments concerning our manuscript entitled “Generalized Neutrosophic Extended Triplet Group” (symmetry-449311). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. Moreover, we have made a thorough revision of the manuscript, including:

1) The English expression has been thoroughly revised, including grammar, spelling, singular and plural, tense and so on.

2) The format of the paper has been revised in detail, including changing some theorems to propositions, citations, proving environment, etc.

3) Some new references have been added and detailed revisions were made in accordance with the reviewers.

Below you will find our point-by-point responses to the comments by red fonts:

 

The authors are dealing with the neutrosophic triplet groups. In this paper, the authors define and discover new results and properties for the generalized neutrosophic extended triplet groups based on semigroup theory.

Ma et al. prove the equality of this group with the quasi completely regular semigroup and the equality of the weak commutative property in this group with the quasi Clifford semigroup.

On the other hand, the authors study the relationships of (Zn, Ä) and neutrosophic extended triplet.

This manuscript is a continuation of the work of the neutrosophic triplet groups developed by coauthor Xiaohong Zhang.

The motivation and justification of the work are appropriate. The paper is well written in correct English. The examples included are adequate.

Response :

We are very grateful to the reviewer’s careful review and pointed out many details for us. We have revised it one by one.

Point 1: Now I include some typographical errors:

Pg. 1, line 32

For: provided in section

read: provided in section 5

Response 1:

Thanks. We have revised this point.

 

Point 2: Pg. 3, line 88

For: the the neutral

read: the neutral

Response 2:

Thanks. We have revised this point.

 

Point 3: Pg. 3, line 92

For: From Theorem 2, we have

read: From Theorem 2, we have:

For the sake of clarity, the following lines can be established in an itemize environment.

Response 3:

Thanks. We have revised this point and use the itemize environment.

 

Point 4: Pg. 4, line: 135

The following condition must be added in as a third condition: commutative generalized neutrosophic extended triplet group

Response 4:

Thanks. We have revised this point.

 

Point 5: Pg. 5, lines: 148-154

For the sake of clarity, these results can be established in an itemize environment.

Response 5:

Thanks. We have revised this point and use the itemize environment.

 

Point 6: Pg. 6, lines: 185 and 186

For: , From Definition 6 and Theorem 7,

read: , from Definition 6 and Theorem 7,

Response 6:

Thanks. We have revised this point.

 

Point 7: Pg. 7, line: 196

For: following hold.

read: following hold:

Response 7:

Thanks. We have revised this point.

 

Point 8: Pg. 7, line: 198

For: respectively. so

read: respectively. So

Response 8:

Thanks. We have revised this point.

 

Point 9: Pg. 8, line: 202

For: GNETG, From Definition 6, for

read: GNETG, from Definition 6, for

Response 9:

Thanks. We have revised this point.

 

Point 10: Pg. 9, line: 212

It could be clearer:

“For any a, b \in N, the following conditions are satisfied:”

Instead of:

“Then a, b \in N:”

Response 10:

Thanks. We have revised this point.

 

Point 11: Pg. 10, line: 220

For: a quasi Clifford semigroup. then there are

read: a quasi Clifford semigroup, then there are

Response 11:

Thanks. We have revised this point.

 

Point 12: Pg. 10, line: 221

For: Applying Definition 10, Being

read: Applying Definition 10, being

Response 12:

Thanks. We have revised this point.

 

 

Thanks again for your valuable comments.

 

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

In this reviewed version of their paper the authors take in account all my suggestions. I consider this paper publishable in the present form.