A Fuzzy-Set Qualitative Comparative Analysis of Publications on the Fuzzy Sets Theory

REVIEWER 1

English language and style are fine/minor spell check required

Following the suggestions of reviewer 1, the manuscript has been revised by a native English speaker to improve the quality of English.

Why the time interval from 1977-2021 is used?

I appreciate your comment, since it allows an improvement in the writing of the manuscript to clarify the methodology and the inclusion criteria in the search, which consequently allows the analysis of articles included in the interval 1977-2021.

When performing the search using the indicated criteria (first and second paragraphs of section 3. Materials and Methods), 1956 articles were found, the first article having been published in 1977. The last article found when performing the search (January 2022), following the restrictions described in section 3, it was published in 2021.

The contributions should be clearly described;

The advantages of this study should be described;

The detailed use of this study should be shown.

The introduction section has been rewritten and now clearly presents the problem under analysis and the advantages of the research. In addition, the abstract and the conclusions section have been rewritten. Now clearly state the contributions of this study.

The recent study should be included.

Following the suggestions, more current references have been included, particularly the literature on systematic literature reviews (eg PRISMA), with articles from 2022.

REVIEWER 2

English language and style are fine/minor spell check required

Following the suggestions of reviewer 2, the manuscript has been revised by a native English speaker to improve the quality of English.

Authors should define their analyzed problem clearly in the introduction section.

The contribution of the paper should be clearly mentioned. It is difficult to see the novelty of the work with respect to the available literature.

Authors should describe more existing studies, focus areas, and problems identified from existing literature.

The introduction section has been rewritten and now clearly presents the problem under analysis. In addition, the abstract and the conclusions section have been rewritten. Now clearly state the contributions of this study.

Following the suggestions, more current references have been included, particularly the literature on systematic literature reviews (eg PRISMA), with articles from 2022.

In Figures 8 and 9, the main term “fuzzy sets and systems” is the biggest. It is obvious since the search was done using this keyword. Is it reasonable to leave it in the figures? It appears as the biggest and connected to all other concepts. I suggest excluding it and viewing what is happening.

Should authors do the cleaning of the initial term set before visualizing it? It is necessary for better visualization and understanding.  For more about the cleaning of keywords you can find in the literature.

Fuzzy sets constitute the core of the research and, as a consequence, the associations presented by "fuzzy sets and systems" vary depending on the intensity (proximity) in the cluster referred to by the reviewer. However, altering the results by subtracting that search term would only return papers that discuss fsQCA in Mathematics (see search criteria: [(“fuzzy set” OR fsQCA) AND mathematics]), that would change the objectives, results and contributions of the study. Thus, the term "fuzzy set" acts as the core of analysis, together with the one that represents the fsQCA methodology, and the term matemathics is presented as a specificity filter that allows delimiting only published articles that are nominally related to mathematics (in title, abstract and/or keywords).

However, figures 8 and 9 (now 9 and 10, since they have been renamed by introducing a new figure 1 at the suggestion of another reviewer) referred to in his comment by reviewer 2, show the degree of association (intensity, closeness): In the first case (previous figure 8; current figure 9), regarding associations according to 4 clusters (fuzzy sets and systems only represent the nucleus of one of the 4 clusters, with blue color). In the second case (previous figure 9; current figure 10), regarding the intertemporal evolution and how the association, precisely of fuzzy sets and systems” is relatively old (2005).

The review should be better structured and guidelines for systematic reviews should be followed.

The literature review section has been rewritten as directed by the reviewer. It now contains sufficient background information and includes all relevant references.

In the abstract, please provide what your review revealed what the results/findings are.

The abstract has been rewritten following the reviewer's instructions.

As MDPI journals follow PRISMA guidelines (see: https://www.mdpi.com/editorial_process#standards ), please try to fit your review in a little more to the PRISMA guidelines.

More information about PRISMA: https://journals.plos.org/plosmedicine/article?id= 10.1371/journal.pmed.1000097

As the reviewer suggests, reference has been made to the PRISMA methodology, as well as the one followed in this article (Thomé et al., 2016). In addition, a diagram (Figure 1) has been constructed that allows understanding the methodological sequence followed by this study.

What are threats to the validity and limitations of the research?

What are future works?

The wording of the conclusions has been improved, emphasizing the threats to validity and the limitations of the research. The reference to future lines of research that should expand the empirical legacy of this article has also been explained more clearly.

The authors should discuss their results in a separate section. How the obtained results can be treated and understood? Why those results are obtained?

As reviewer 2 suggests, a specific discussion section has been built. The wording of this section of the manuscript has been improved to facilitate the understanding of the results obtained and, in particular, the understanding and implications of these results.

REVIEWER 3

English language and style are fine/minor spell check required

Following the suggestions of reviewer 3, the manuscript has been revised by a native English speaker to improve the quality of English.

Author gave a bibliometric analysis of fuzzy theory within  the field of  mathematics. In this case, IEEE TFS and other journals are not considered. This is not necessarily a bad thing. This can help to focus the reader on  math-driven fuzzy sets and fuzzy logics .

1， There exist “Fuzzy-Set，fuzzy-set，Fuzzy set，fuzzy set” 。

2，Page 1 L30， “its applications to multiple related areas. ted withengineering and management.”？

3，Page3 L104， ”fuzzy-set, fuzzy-logit“

4，Page14 L429， ”decisión-making“ 

5， Page24 L640， ”Fuzzy soft $$$\backslash$beta $$ $β$-covering ”

Please check again.

I appreciate your kind comment. The search criteria includes all journals indexed in the Web of Science core collection, without taking additional inclusion or exclusion preferences.

1. In fact, all the combinations that, due to proximity, could include the fuzzy-set terms are used, just as the researchers present them in the keywords, keywords plus, abstract or title. All the terms were used to include the total number of articles and not to underrepresent any research for having used some variant such as those indicated.

2. Fixed a typo, the text now reads: “related whith engineering and management”.

3. Fixed a typo, the text now reads: “fuzzy-logic”

4. Fixed a typo, the text now reads: “decision-making”

5. The title of the cited research is now correct (there was a typographical problem), after the modification it says: “Fuzzy soft β -covering based fuzzy rough sets and corresponding decision-making applications”

REVIEWER 4

Extensive editing of English language and style required

The manuscript must be revised in format and presentation. This includes a complete review by an English native.

Following the suggestions of reviewer 4, the manuscript has been revised by a native English speaker to improve the quality of English.

For instance, in the title, and all over the text, "Fuzzy-sets" do not need the capital F and neither a dash in the middle. Conversely, the "Fuzzy Sets Theory" (FST) needs capitalization since it is a name; “fuzzy-set Qualitative Comparative Analysis” needs the dash, since fsQCA is a type of QCA.  

My gratitude to reviewer 4 for his suggestions. The manuscript has been improved with all the contributions of the reviewer.

The Abstract also has a bad presentation, including an unnecessary ® after Web of Science (WOS). Confusing among database (the whole WOS) and dataset (a part of it). But, what bothered me more were the N=1956 (variable in italics, please) and the fsQCA.

The manuscript has been adjusted with all the suggested improvements.

2030 Agenda is lost in the Abstract.

Following the reviewer's suggestion, mention of 2030 Agenda has been removed. Since it was not of great importance, the manuscript only refers to the 2030 Agenda when explaining the context in which the Sustainable Development Goals (SDGs) arise.

The Introduction is a bad start. Too short. No context. Why did the searched range begin in 1977, since FST was proposed in 1965?

The structure of the introduction section has been improved, expanding it and offering a better presentation of the topic.

The date range resulting from the search according to the articles located according to the specific search criteria applied is also better explained, clarifying the reason for not including other seminal articles. Specifically, the text has been redrafted: “Figure 1 shows the review methodology applied in this article. The first search returned 1989 results. The application of quality and contextual threshold performs an evaluation of the search results, in-depth review and residual search, configuring a database of 1956 articles. The search did not add articles that did not meet the required co-occurrence, according to the boolean search: [(“fuzzy set” OR fsQCA) AND SU=mathematics], only SSCI or SCI-Expanded. Therefore, if an article did not meet both requirements, it was not included in the database of this study, even in the case of seminal articles on Fuzzy Sets Theory, whose origin dates back to 1956, that is, two decades prior to the first article located.“

The second section, Theoretical Framework, is also confusing, with methodological contents. Page 3, ''the proposed model'' is presented. I am sorry, this is not a model. It looks more like an equation, poorly presented for a scientific journal. Are YEARS, NIY, UC... variables? fuzzy sets? It is not clear.

When the theoretical framework refers to fsQCA, it does not focus on the methodology but on its representativeness of this method in the academic publications studied through the bibliometric study.

The theoretical framework has been rewritten to clarify that the proposed causal model is not mathematical but rather configurational, according to Ragin (1987). However, following the reviewer's suggestion, it has been renamed to Equation 1.

The methodology section now clearly explains the variables that are calibrated according to the methodology proposed by Ragin (1987) and are transformed, taking values belonging to fuzzy sets, and the following text has also been included: “After the calibration process, the values of each variable are configured in fuzzy sets.”

The manuscript has only one author. Therefore, identifying author contributions before the appendices is not necessary. In the same context, adding "Source: authors’ elaboration." below figures and tables is unnecessary. Otherwise, an abbreviation list is missing, since the manuscript does extensive use of acronyms.

Suggested modifications have been made to improve the manuscript.

On the contents, first, it is necessary to choose the manuscript purpose. The purpose is to present a bibliometric analysis on FST? Or the purpose is the proposal of a model? This clarification requires changes in title, abstract, and Introduction. The word “Mathematics” in the title is out of context, seeming an appeal to the journal’s name.

A better title would be “A fuzzy-set qualitative comparative analysis of publications on the Fuzzy Sets Theory”. Replace the last paragraph of the Introduction starting from “This research is structured as follows…” to “This work is structured as follows…”, since the manuscript is not one research, but a paper on one research.

This paragraph shall be kept at the end of Section 1. But, before the last paragraph, the first paragraph of section 2 shall be moved and inserted in the Introduction, deleting the title of Section 2 Theoretical Framework. Therefore, the Introduction will provide “sufficient background and include all relevant references” as the guidelines for the journal. New Section 2 Materials and Method shall start with the paragraph “Authors such as Ragin [13]…”. Emphasis on method is required. Therefore, a flowchart like Fig. 1 from Ref. [21] will be useful. After “the model”, IMP = f (YEARS, NIY, UC, CRC, SUST, OA), which should be referred to as Equation 1, some exception or the whole Appendix B shall be inserted.

The suggested changes have been made to the title, abstract and introduction. In addition, section 1 has been merged with section 2, allowing the background and included references to be presented in a more relevant way.

The model has been modified, renaming it as Equation 1. The exception and Appendix B are included in the results section with the complete report of results calculated by the Quine–McCluskey Algorithm, according to equation 1.

At least one brief explanation, of Quine–McCluskey Algorithm.

One brif explanation of Quine-McCluskey Algorithm has been incorporated in the methodology section.

REVIEWER 1

(x) English language and style are fine/minor spell check required

The manuscript has been revised by a native English speaker to improve the quality of English.

REVIEWER 2

(x) English language and style are fine/minor spell check required

The manuscript has been revised by a native English speaker to improve the quality of English.

The authors have improved the paper. However, some minor revisions should be done.

1. Figure 1 should be improved using some notation, like block chine or similar. Now, it is not clear. It is not clear what the different symbols represent. Is it the flow of activities, the flow of results?

The manuscript has been improved, including the writing of a detailed description of Figure 1 after its inclusion in the article, and it is now possible to follow the activity workflow and results obtained.

2.     What are the inclusion and exclusion criteria for papers?

The wording of the manuscript has been improved to clarify the inclusion and exclusion criteria. Specifically, it has been explained more clearly in the methods section. In addition, the header of Figure 1 includes a box that reports the database (Web of Science Core Collection) and the selection criteria (keywords, type of document, subject journal and index: SCI or SCI-Expanded)

3.     I suggest excluding the keyword "fuzzy set and systems" from Figure 9 and Figure 10 to view the real picture of keywords. It is obvious that this keyword is the highest because it has been searched and will appear in all results. For the reader, it is more interesting other keywords

I must point out that, strictly speaking, “Fuzzy Set and Systems” is not a keyword, but the title of a journal (the most relevant for that cluster). Therefore, Figures 9 and 10 show the bibliographic coupling for journals and do not show clusters of keywords.

Thus, Figure 9 offers the connection grouping between journals in different colors under the criterion of bibliographic coupling (and shows the network visualization). In this sense, the size of the titles of the journals corresponds to their relevance in terms of analysis of this research. In this case (see Table 6; Appendix A), the journal referred by reviewer 2 (Fuzzy set and Systems) is the one with the greatest impact (19 high-impact articles out of the 25 articles with the greatest impact), and this helps to explain the size of the text inside the Figure.

On the other hand, Figure 10 shows the same connections (coupling for journals), but the grouping of colors does not correspond to the connection networks between journals, but rather in overlay visualization, so the intertemporal evolution of these connections between journals is shown. journals: oldest bibliographic coupling with continuum of darker colors (from purple); newer bibliographinc occupancy with the continuum of lighter colors (up to yellow).

In another example, Figure 9 and Figure 10 show a text size of Mathematics (which, as I say, refers to this MDPI journal, and not to the scientific-mathematical term) is larger than “Applied and Computational Mathematics”, among other journals.

REVIEWER 4

(x) Moderate English changes required

The manuscript has been revised by a native English speaker to improve the quality of English.

The author addressed the main comments or corrections I required. Manuscript has been improved to publication level.

My only minors concerns is the absence of an acronymn list in the end, and the lack of Quine--McCluskey Algorithm.

Following the reviewer's suggestion, an acronym list has been added at the end of the manuscript (Appendix C), just before the references section.

It was cited in Sec. 3.2.2, but I believe that a flowchart or some other detail would be very useful for readers.

An example has been introduced in section 3.2.2 to clarify the function and procedure followed by the Quine-McCluskey Algorithm during the minimization process. The example clarifies how the algorithm contributes to solve and optimize the problem with a devising a general mechanical procedure for reducing any formula to its simplest equivalent, starting from an example based on QCA's “truth table”, using a three-term primitive Boolean equation.