M-Hazy Vector Spaces over M-Hazy Field

Round 1

Reviewer 1 Report

This paper is an attempt to define fuzzy vector spaces and fields with operators that are fuzzy (i.e., the result is computed up to some degree). Their approach is based on the idea that an operator ∗  is a function ∗:P x P --> (P--> M). Thus if x, y ∈ P and  x ∗ y = z in "classical" sense, then (x  ∗ y)(z) = m. This of course could be simplified. My only concern here is that final result depends on the function  (x  ∗ y) and one has to define many such functions, which is a bit problematic.

Section 3 could be skipped as it contains propositions that are proved elsewhere. Apart from that, I have no other comments. Of course I cannot check the validity of the proofs in just one week. One needs at least one month to check things properly.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

See attachment.

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 3 Report

Dear Authors,

The structure of this paper and study results are presented in an appropriate style. However, there are some drawbacks. The English is poor and needs drastic review. 

Why is this topic important? Define the motivation for your study.

Although the results are mathematically true, the level of the results is very simple. I expected more than these. Hence, not very deep results without the explanation why these results are important, can not satisfy me to accept this paper. At least one of them should be highlighted.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

Dear Authors,

With these changes, it looks much better. Now I can recommend it to publish.