A Bibliometric Overview of the Field of Type-2 Fuzzy Sets and Systems [Discussion Forum]

Fuzzy Sets and Systems is an area of computational intelligence, pioneered by Lotfi Zadeh over 50 years ago in a seminal paper in Information and Control. Fuzzy Sets (FSs) deal with uncertainty in our knowledge of a particular situation. Research and applications in FSs have grown steadily over 50 years. More recently, we have seen a growth in Type-2 Fuzzy Set (T2 FS) related papers, where T2 FSs are utilized to handle uncertainty in realworld problems. In this paper, we have used bibliometric methods to obtain a broad overview of the area of T2 FSs. This method analyzes information on the bibliographic details of published journal papers, which includes title, authors, author address, journals and citations, extracted from the Science and Social Science Citation Indices in the Web of Science (WoS) database for the last 20 years (1997-2017). We have compared the growth of publications in the field of FSs, and its subset T2 FSs, identified highly cited papers in T2 FSs, highly cited authors, key institutions, and main countries with researchers involved in T2 FS related research.


I. Introduction
Data in the real world is gathered from many sources. Considering that none of the processes in the real world is 'ideal', the data collected generally possess some kind of uncertainty, and information about some features or characteristics of the data are either incorrect or incomplete. Uncertainty is, therefore, a major challenge in real world applications, and there was a need felt, to have a theoretical framework within the discipline of Mathematics and Computer Science for handling such unknown, incomplete or uncertain information. 1 A solution was provided by Zadeh [1] in 1965 when he proposed the fuzzy set theory to bridge the gap between certain and uncertain environments. Although Zadeh's work did not attract much attention initially, from the mid-70's a number of scientists began examining this area. Several professional associations were started, and the first conference was held in USA in 1982. European and Asian researchers had also started to show increased attention to the field since the mid-70's. In 1985, the International Fuzzy Systems Association (IFSA) was created which held its first conference in Palma de Mallorca, in Spain. Today, fuzzy set theory has emerged as a powerful way of quantitatively representing and manipulating the imprecision in a variety of problems, both theoretical and applied. It is now an established field with thousands of researchers studying different theoretical or practical aspects, as can be verified by bibliometrics.
Bibliometrics (equivalently scientometrics) refers to a technique of statistical analysis of scientific papers, using only bibliographic details or meta-data on papers, as is available from citation indexes such as Web of Science (WoS) or Scopus. It enables extraction of many features in the scientific field to which the papers belong, without actually reading the entire corpus. To extract the papers in a field, a suitable keyword or string is used to query the WoS database. Care needs to be taken at this stage to ensure that the query retrieves all relevant information, and ensures that both precision and recall are high. The data has information on papers, including title, author names, journal, publication year, author address and citations. This can be analyzed to obtain a measure of the productivity and citation of authors, institutions or countries. From the citation data, one can obtain highly cited papers, or authors, journals, institutions and countries that publish the most cited articles. Time trends can also be obtained. Bibliometric analysis has been performed in different disciplines.
The first bibliometric analysis and mapping of Fuzzy Sets (FSs) research were done by Herrera and co-authors in 2009 for Spain, a country that held a leading position in fuzzy research at the time [2]. In 2011, the same Spanish group analyzed the entire field covering research in fuzzy set theory in all countries [3]. An overview of the origin of FSs, journals used, prominent authors, and research can be found in a later study by Merigo, Gil-Lafuente and Yager in 2015 [4]. Van Eck and Waltman [5]- [6] have mapped the related field of Computational Intelligence in 2006 and again in 2007. Recently, Bustince has also studied the history of various types of FSs in [77]. Other Computer Science fields have also been covered, e.g., big data [7], linguistic decision making [8], Atanassov intuitionistic fuzzy sets [9], Industry 4.0 [29], fuzzy decision making [10], etc. Apart from subject wise bibliometric analysis, there are also journal specific studies in the literature, e.g., [11]- [13], [48]- [52].
Type-1 (T1) FSs are limited by the certainty of their membership function (MF) values, something that was already recognized by Zadeh [24] when he introduced type-2 (T2) FSs, whose MF values are no longer certain but are modeled as intervals that can be uniformly or non-uniformly weighted. A T2 FS is characterized by its footprint of uncertainty (FOU), bounded by two T1 MFs, called lower M F (LMF) and upper MF (UMF). Although T2 FSs were first introduced by Zadeh in 1975, it was Karnik and Mendel [22] who first introduced T2 fuzzy logic systems (FLS) in 1998. For a history of why it took so long for this to happen, see [79].
T2 FSs have been used extensively by many researchers in a broad range of applications in which MF uncertainties are modeled by their FOUs as a way to handle application uncertainties completely within the framework of FSs (e.g., [14]- [16], [18]- [25], [43]- [46], [53]- [76]). To get a better overview of the overall research on all aspects of T2 FSs and systems, see [55] which lists more than 1,000 articles, and was recently made public by Mendel. The trends in research publications indicate that the overall field of fuzzy sets and systems has grown from around 1,648 publications 2 in 1997 to around 9,130 publications in 2017. During the same period, T2 publications have grown from almost none to more than 230. Comparing the two growth rates during the past 10 years, it would seem that the T2 FS field has been growing faster than the overall FS field, which has motivated the present scientometric study. Fig. 1 shows a comparison of the percentage growth 3 in the T1 and T2 fuzzy fields. When we take a closer look at the two curves, we can conclude that the percentage growth for T2 fuzzy was very dynamic during the early years but is now approaching the percentage growth of the entire FS field, implying that the T2 field is no longer an emerging technology but has matured. 4 Therefore, it is worth pointing out that the T2 field should no longer be referred to as an emerging field.
The main contributions of this study are given below: 1) It provides a detailed bibliometric analysis of all the publications on T2 FSs and systems as indexed in WoS core collections Science Citation Index-Expanded (SCI-E), Social Sciences Citation Index (SSCI) and Emerging Sources Citation Index (ESCI) database. 2) It is the first such work that has analyzed the key contributing authors on T2 FS related research and their institutions.   These counts are annual, and T2 publications are not included in these counts. 3 The percentage growth is calculated as: Percentage growth = ((A−B)/B) × 100%, where A = Publications (current year) and B = Publications (previous year). 4 One might also disagree with this statement, since the number of publications of the T2FSs are largely behind that of the FS field, according to the WoS data. A possible reason for the latter might be that T2 FSs have not yet been explored much by the researchers of other fields, as compared to the primary domain of T1 FSs.
3) It also provides the topmost venues (journals) which are chosen by the key contributors to publish their research work on T2 FSs and systems. 4) It discusses the top 20 most highly cited articles on T2 FSs. 5) It also analyzes various aspects of the contributions from different countries. 6) It provides the co-authorship analysis of T2 FSs related research. This paper is organized as follows: Section II discusses data collection and methodology; Section III provides scientometric analysis and quantitative results on research growth, discipline, top source journals, most productive and highly cited authors, and highly cited papers; Section IV covers a countrywise analysis along with analysis of institutional performances. Finally, Section V concludes this paper with discussions on findings of the study and its future scopes.

II. Data Collection and Methodology
Bibliographic details of research outputs (articles, reviews, proceedings papers, etc.) were collected from the WoS index using the query term 5 "Type-2 Fuzzy" till December 31, 2017. All the papers in which this term is present in any of the three key locations: Title, Abstract, and Keywords are extracted. The query term "Type-2 Fuzzy" was chosen since it covers 'Type-2 Fuzzy Sets' as well as its two common variants: 'General Type-2 Fuzzy Sets (GT2 FSs)' and 'Interval Type-2 Fuzzy Sets (IT2 FSs).' 6 Databases included in our search were the SCI-E, SSCI and ESCI. The data corresponds to the duration of 20 years from 1997 to 2017.
A total of 1,288 papers were retrieved with a total of 35,072 citations. Each of the records consisted of 66 Fields, such as Author(s), Affiliations(s), Title, Abstract, Citations, Source, etc. for each paper. Cited references were also collected for these publications. The data was pre-processed manually to eliminate duplicate/outliers so that only unique records remained in the extracted data. Then, the data was processed programmatically in R. In all calculations, we used integer counting 7 ; i.e., when there was a co-authored paper, each author was credited with one paper. This was also done for institutions and countries.

III. Analysis and Results
The following scientometric analysis and results are given in the subsequent subsections: (A) Qualitative Analysis, (B) Discipline wise Analysis, (C) Top Source Journals, (D) Most Productive and Highly Cited Authors, (E) Most Cited Papers, and (F) Keywords Visualization using VOSviewer [80].

A. Qualitative Analysis
A qualitative and visual analysis of the data usually precedes detailed analysis. After noting the growth pattern of the T2 fuzzy research area, we note the level of citations. We found that 1,157 papers out of 1,288 papers were cited, constituting 89.82% of the total. This is indicative of an active field. There are 131 un-cited papers, but they also include recent papers, from the past one year or two. Among the cited papers, most of the papers were cited only 0-50 times (993 papers or 77.1%) while only 7 papers had more than 500 citations.

B. Discipline Wise Analysis
As expected, Computer Science as a broad category, contains the maximum number of papers in the domain of T2 FSs with 905 papers, followed by Engineering, (503 papers, 39.05%), and Automation Control Systems (167 papers, 12.97%). Mathematics papers cover only 9.16% of the field with 118 papers.
There are in fact 149 distinct subject categories in the data indicating that the applications are widely dispersed across different areas. The papers may be assigned to more than a single category indicating interdisciplinary work.

C. Top Source Journals
In the case of top contributing journals in the field, parameters taken into account are the Total Publication (TP) count, Total Citation (TC) count, and Cites/Paper. One more parameter, h-index is also computed for visualizing the impact of these sources; it is the number of publications (N) that have attained more than N citations for the number of cited papers.
The journals with the most T2 papers are IEEE Transactions on Fuzzy Systems and Information Sciences (TP > 100 papers) and Applied Soft Computing (TP > 50 papers). IEEE Transactions on Fuzzy Systems is also the most cited journal with total citations being 10,737 in 20 years, or about 537 citations per year on average. It is cited almost twice as frequently as the next most frequently cited journal in the field, Information Sciences (TC = 5,864). Other journals with more than 1,000 citations in 20 years are Expert Systems with Applications (TC = 1,872) and Applied Soft Computing (TC = 1,664), Fuzzy Sets and Systems (TC = 1,290) and IEEE Computational Intelligence Magazine (TC = 1,060). Table 1 provides the top 15 journals with the highest number of publications.
If we look at the size-independent indicator, citations per paper (Cites/ Paper), another set of journals emerges which have high citations but with relatively few papers. Physica A with a single paper has 113 citations. IEEE Transactions on Systems, Man and Cybernetics with 93.5 cites per paper, was followed by IEEE Transactions on Fuzzy Systems with 74.56 cites per paper. Note that most journals which published T2 papers are not core fuzzy journals. The only core journal for fuzzy papers is IEEE Transactions on Fuzzy Systems. This highlights the fact that not only theory but also applications of FSs have also been highly cited even when they are published in small numbers and are dispersed in journals outside the field of FSs.
If we use the h-Index as an indicator for T2 FS publications, the journals with the highest h-Index are seen to be IEEE 5 For traditional FSs we have used the keyword "Fuzzy" for the search in the WoS. 6 IT2 FSs are closely related to (some even say they are generalization of) Interval-valued fuzzy sets (IVFSs) [78]. If the papers on IVFSs have used the keyword "type-2 fuzzy" in any of these key locations (Title, Abstract, and Keywords), then they are automatically included. Papers that didn't use the keyword "type-2 fuzzy," in any of the three key locations were excluded.

D. Most Productive and Highly Cited Authors
Results for the most productive authors in research in T2 FSs are discussed in this section. As can be seen from Table 2

E. Highly Cited Papers
This section lists the top 20 highly cited papers in T2 FSs, dates ranging from 1999-2012. The highest citation till now for a T2 FSs paper is by Mendel and John, written in 2002, titled 'Type-2 fuzzy sets made simple' [17] which received 1,129 citations.
Usually, reviews are more cited, but this does not seem to be the case here. Of the 20 highly cited papers, as many as 11 are in IEEE Transactions on Fuzzy Systems, with an impact factor IF = 8.415. Twelve (12) papers have been authored/co-authored by Mendel. This is the highest number of papers by any individual in this elite set. Nine Among the top 20 cited papers (see Table 3), the 2002 paper [17] from Mendel and John has the highest citations per year of 75.27. It is followed by  (2), Liang (2), Liu (2). The numbers in the brackets denote the number of papers by the respective authors in the top 20 highly cited publications.

F. Keywords Visualization Using VOSviewer
A visualization of research intensity of different areas within T2 FS for the entire period (1997-2017), using the visualization software VOSviewer [80], is shown in Fig. 2. Red areas indicate high research intensity as in a 'heat map.' Keywords 'type-2 fuzzy set/s,' 'type-2 fuzzy logic,' and 'interval type-2 fuzzy set' lie in the red areas. These are the most frequently used keywords/topics in the papers of type-2 fuzzy research. The other relative hot spots are: 'uncertainty,' 'fuzzy control,' and 'fuzzy sets.' The positions of the research areas are determined by the co-occurrence frequency of the keywords.

IV. Country Wise Distribution
Many countries have researchers working in the area of T2 FSs. Here we study various aspects of the contributions by researchers from different regions/countries. It includes country wise distribution, time dynamics, impact analysis, institution analysis, etc.

B. Impact Analysis
In this section, we analyze the quality of the publications (measured in terms of citations) by researchers from different countries, divided into four periods

C. Growth Rate
T2 FSs originated in the USA and researchers in the country published the largest number of papers in the initial 15 years. The number of papers from the researchers in USA has declined in recent years while researchers in other countries like China and Taiwan have published more. In Fig. 4, we see the total production plotted against the average annual productivity growth in T2 FSs for researchers in different countries. Researchers in China have published the largest number of papers (>200) and also has a fairly high growth rate of 15.5%. Researchers in Iran have shown a considerably higher growth rate of 13.4% in the last decade.
However, researchers in USA and Taiwan have more than a hundred papers each but the growth rate has been low (5% for Taiwanese researchers and -22.3% for researchers in the USA). Publications by the researchers in UK also have a low growth rate of -8.3%. Works published by the researchers in Turkey, Mexico, and India have grown at the rate of 6.7, 1.7, and 6.5 percent, respectively. Papers by researchers in the USA, which has been at third position among all other countries, saw a decline of growth rate in recent years and is currently showing the lowest growth rate among the top 20 countries. This is mainly because of Prof. Mendel's retirement, since he was continuously contributing in earlier years.

D. Institutional Performance
This section discusses the Top 20 Universities or Organizations in T2 FS research. As available in Table 4, the top institution is the University of Southern California, researchers from which contributed 5.7% to the published papers in T2 FSs. It is the only institution from the USA in the top 20 list. It also happens to have the highest number of citations (10,104  University of Southern California, USA. His citation counts are almost the same as that of his university. Castillo from Tijuana Institute of Technology contributed 90.77% to pub-lications and 96.26% to citations of that institute. After University of Southern California, the highest citations per paper (ACPP = 105) were found for De Montfort University for which the main contributor was John. The next highest citations per paper were obtained by Essex University in the UK, where Hagras was the main contributor.

F. Co-Authorship Study
It can be seen from Fig. 5 that the main actors have their own groups of coauthors as shown using different colors. Mendel, John, Hagras, Kumbasar, Bustince and Kaynak appear as the main characters in the interconnected clusters seen on the left. On the right is an independent cluster with few connections to the other cluster, with Castillo and Mendez as the main characters. The interconnection between the left and right nodes represents the connection between the authors of both sides.

V. Discussions and Conclusion
In this study, we have characterized the field of T2 FSs which has developed within the parent discipline of FSs. T2 FSs is a relatively new field, having originated only about 43 years ago in the USA (in 1975). The top 20 highly cited papers span about 14 years, from 1999 to 2012 indicating the importance of this period for the discipline. Twelve papers in this set of 20 are (co-) authored by Mendel. He has both the highest number of papers and by far the highest citations in the field. Out of the authors with more than 10 TP, Mendel has the second highest citations per paper (~142.16), the highest being ~157.72 cites per paper obtained by John.
Among the top countries with researchers doing research on T2 FSs, we find China, followed by Iran, USA, and Taiwan. Papers published by the researchers in the USA have the highest total citations. Citations of the publications by Chinese researchers in the most recent period were the highest. Although researchers in China have produced the highest number of publications, there are only two Chinese institutions contributing to the top 20 list at ranks 11th and 16th with a total of 3.18% share. This implies that T2 FS research in China is distributed across a number of institutions. Taiwan has four institutions contributing to a total share

FIGURE 5
Co-authorship structure of the field of T2 FSs. of 6.06%. There are three institutions from Iran which contributes of 6.28%. Two institutions are from Mexico with % share of 7.07%. The field appears to have a dual structure with a small well-defined core of papers published in a few prominent and specialized journals, and a dispersed periphery of papers linked to applications which are spread out over a large variety of journals. There is a large potential for growth in application areas.
While WoS has a good coverage of journals, it may not cover all journals or proceedings of conferences-particularly the latter, which are considered to be an important contribution in Computer Science. Consequently, any paper published in a journal or proceedings not indexed by WoS were overlooked, even if important, in this study. Therefore, a very good future scope of this scientometric study would be to consider other indexing platforms such as Google scholar and Scopus for a thorough comparison with the WoS.