The Extended Minimax Disparity RIM Quantifier Problem

Round  1

Reviewer 1 Report

Overall a good paper, here are some comments to improve the paper: 1. Abstract: In the Abstract do not use formula 2. Introduction: In line 4 of the Introduction you referred to [1–8,10,14,15,19–24], however this is no useful to readers. Researchers can easily see all OWA papers in the recent bibliography published in Yager’s journal International Journal of Approximate Reasoning [Emrouznejad, A. and Marianna Marra (2014), Ordered Weighted Averaging Operators 1988–2014: A citation-based literature survey, International Journal of Intelligent Systems, 29:994-1014] 3. Literature referred to "Computers & Industrial Engineering 50(2006) 312-316" but later Amin improved the ordered weighted averaging which has been ignored here Amin, G. R. (2011). Parametric aggregation in ordered weighted averaging. International Journal of Approximate Reasoning 52(6): 819–827.] 4. Section 3, line 65: “The minimum variance problem for OWA operator can be extended to the RIM” quantifier” should be “The minimum variance problem for OWA operator is extended to the RIM quantifier” 5. Page 4, last line it is claimed that “max |wi-wj| = max wi - min wi. Why? Not that i is between 1 to n-1 while j is between i+1 and n. 6. I suggest adding a new section 6, and add a numerical example or an application, perhaps you can compare the results with previously published papers. 7. Add a new section and include conclusion 8. Reference: name of authors ar3 missing in reference 8 References: • Fullér, F. P. Majlender, On obtaining minimal variability OWA operator weights, Fuzzy Sets and Systems, 2003 136, 203-215. • Emrouznejad, A. (2008). MP-OWA: The most preferred OWA operator. Knowledge-Based Systems 21(8): 847-851 • Liu X., H. Lou, On the equivalence of some approaches to the OWA operator and RIM quantifier determination, Fuzzy Sets and Systems, 2007 159, 1673-1688.

Author Response

Please see attached file. Thank you.

Author Response File: Author Response.pdf

Reviewer 2 Report

The author introduces a continuous extension of an extended minimax disparity OWA model,  which is the extended minimax disparity regular increasing monotonic quantifier problem, under given orness level and proves it analytically.

The mathematics is sound, a well-written paper.

Author Response

Thank for reviewing my paper.

Reviewer 3 Report

In the paper extended minimax disparity model for RIM quantifier determination under given orness level is proposed and prove analytically.

The author proposed a new solution and proved it. Unfortunately the advantages of his proposal in relation to other solutions were not commented on in any way. The article gives the impression of being cut. Before publication, the advantages of his proposals and conclusions should be added.

References look outdated, except for the author's articles. Newer items should be added to the article. Writing about the 2006 article (line 32): "has been recently introduced" may mislead the reader in 2019. Please delete “recently”.

Author Response

* I added conclusion section.

* There are many important old mathematical problems which have not been proved so far. Solving unsolved problem is a good research topic. This ia one of the advantages of my proposal.

* I added two new articles: 2014, 2008.

* I deleted "recently".

Round  2

Reviewer 1 Report

In line 23, please remove "?":

[1–5,7,8,10,14,21? –24]. should be written as

[1–5,7,8,10,14,21–24].

Reviewer 3 Report

The author took into account the comments of the reviewer. After the revision, the article is worth publishing.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.