Abstract
Since proposed in 1983, the intuitionistic fuzzy set (IFS) theory has grown immensely during the past decades and has wide application in machine learning, pattern recognition, management engineering and decision making. With the rapid development and widespread adoption of IFS, thousands of research results have been appeared, focusing on both theory development and practical applications. Given the large number of research materials exist, this paper intends to make a scientometric review on IFS studies to reveal the most cited papers, influential authors and influential journals in this domain based on the 1318 references retrieved from SCIE and SSCI databases via Web of science. The research results of this paper are based on the objective data analysis and they are less affected by subjective biases, which make them more reliable.
Introduction
Bulgarian scholar Atanassov extended the traditional fuzzy set (FS) [74] and proposed the intuitionistic fuzzy set (IFS) in 1983 [1]. It is better than FS in dealing with the vagueness and fuzziness of the real world. So far, IFS has been proposed for over thirty years and it receives more and more attentions from scholars and practitioners year by year. IFS has been successfully applied to machine learning [52], pattern recognition [10, 18], management engineering [36, 34] and decision making [38–43, 79] etc. Given this sustainable and stable growth of IFS field, it is urgent and necessary to make a comprehensive review and find out the development path in IFS area. Doing so would offer obvious advantages, for example it allows the new researchers to understand the developments trends and possible direction quickly, and provides reference for their scientific research topics.
It is noted that some scholars have made some surveys related to one specialized aspect of IFS, such as the survey of decision making approaches with intuitionistic fuzzy preference relations given by Xu and Liao [64], the survey of applications of IFS given by Xu and Zhao [67], the research of the development of IFS based on citation network analysis [71]. However, there is no any paper to review the IFS theory and illustrate the state of the art of IFS theory through visualization and quantitative research. The purpose of this paper is to take full advantage of bibliometric analysis [9, 70] and make a scientometric review on IFS study with the help of a useful visualization and analysis software called CiteSpace which was developed by Dr. Chen Chaomei [13, 14]. The main characteristics of this paper can be summarized as follows: It is based on a large number of references. A total of 1318 references which was downloaded from SCIE and SSCI databases via Web of Science were used for analysis in this paper. All the research results of this paper are based on the objective data analysis and they are less affected by our subjective biases which make them more reliable.
The structure of this paper is organized as follows: Section 2 studies the current status of IFS researches, and then the data retrieval strategy of this paper are presented in this section. Section 3 makes analysis on the most cited references, the influential authors and the influential journals, respectively. Summarization of the research findings and the conclusion of this paper are given in Section 4.
Current status of intuitionistic fuzzy studies
Web of Science is a large-scale integrated, multidisciplinary, core journal citation index database [44]. It is an excellent information retrieval tool which is based on the user’s needs and imagination. In this paper, we retrieve literatures in SCIE and SSCI databases via Web of Science. We take “intuitionistic fuzzy” as topical retrieval on Web of Science and the time span is defined as “all years”. In this search strategy, we obtain 1318 records. The top 10 countries (regions) contributing the researches on IFS are shown in Table 1.
Table 1 shows that China contributed the most publications on IFS (634 publications) and accounted for about half of the total. Occupying the second position is India with 135 publications followed by Iran, Spain, Turkey, Taiwan, USA, Poland, South Korea, and Bulgaria. The top 5 journals publishing the articles on IFS are Journal of Intelligent & Fuzzy Systems, Information Sciences, Fuzzy Sets and Systems, International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, and Expert Systems with Applications. The top 10 journals are listed in Table 2.
Table 3 shows clearly that, Xu Zeshui (Sichuan University, China), Li Deng-Feng (Fuzhou University, China), Glad Deschrijver (Ghent University, Belgium), Chen Xiaohong (Central South University, China) and Bijan Davvaz (Yazd University, Iran) published the top five numbers of articles on IFS.
Visualization and quantitative analysis on the development of IFS
The citation analysis is a very critical method for studying the research trends of IFS. Based on the citation analysis, the references with most citations, authors and journals with important influence in the research of IFS area can be singled out. In order to avoid the influence of subjective thought, a useful visualization and quantitative analysis technique called CiteSpace is adopted to aid the study of IFS research. Since IFS was proposed in 1983 [1], we set the timespan as 1983–2015. In this paper, we used some significant indicators such as “Centrality”, “Burst” and ‘Half-life’ which are key indicators for CiteSpace. We do not present the meaning and function of the above three indicators. Readers can refer to the references in detail [13, 77].
Most cited references
Table 4 shows the top 30 cited references on IFS studies. It tells that the top one cited reference is Intuitionistic fuzzy sets published by Atanassov [2] with frequency of 900 in our dataset. From Table 4, we also found that there are 12 references in the total of 30 articles published on Fuzzy Sets and Systems. This signals the truth that Fuzzy Sets and Systems was an important outlet for the research results of IFS.
Figure 1 shows the main references clusters in IFS field. It tells us that the vast majority of the cited references are gathered together and they are around the center of the most cited reference [2]. From Table 4 we found that, the majority of the most cited references (4 of 5 top cited references, 12 of 15 top cited references; 20 of 30 top cited references) were published more than 10 years ago.
The paper named “Intuitionistic fuzzy sets” was published by Atanassov on Fuzzy Sets and Systems in 1986. In this paper, Atanassov first made systematical description of “intuitionistic fuzzy set” which was defined as a generalization of “fuzzy set”. Although this article has been published for nearly 30 years, it is still receiving increasing attentions. This paper has a profound impact on IFS study.
“Fuzzy sets” is a very classical paper published by Zadeh on Information and Control in 1965. Since the IFS is a generalization of FS, a lot of theories about IFS were put forwarded in the motivation of FS theory. Therefore, this reference [74] received a very high number of citations in IFS area.
The book named “Intuitionistic fuzzy sets” was completed by Atanassov in 1999. It makes a comprehensive and complete report regarding to IFS theory and also reported that IFS has been applied to diverse fields [6].
“Interval valued intuitionistic fuzzy sets” is a very important research result accomplished by Atanassov and Gargov and published in the journal of Fuzzy Sets and Systems in 1989. In this paper, the authors proposed a generalized form of IFS theory and introduced the interval-valued intuitionistic fuzzy sets.
The paper named “Intuitionistic fuzzy aggregation operators” was published on IEEE Transactions on Fuzzy Systems in 2007, which was the research results of Xu ZS from China. In this paper, the author developed some intuitionistic fuzzy information aggregation operators and applied them to multi-attribute decision making problems.
One thing is certain: the reference [2] plays a crucial role in the development of IFS theory although the concept of this theory was not put forwarded in this reference. Furthermore, as shown in Fig. 2, some breakthrough researches in IFS area were achieved after 1986 and some fundamental researches were received in 1980s–1990 s. However, our research results show that there are no very excellent achievements appeared after 2007 (Fig. 3). But it is essential to recognize that the new research results should took a long time to be widely recognized by academic circles. It is possible that some new research results could become very influential in the future.
Influential authors
During the analysis process, we found that some different nodes in the networks on behalf of the same author actually. For example, three different kinds of node in the network such as “Atanassov KT”, “Atanassov K” and “Atanassov KT” are all represent the same author, so they should be merged into “Atanassov KT”. The same situation is reflected in the “Xu ZS”, “Xu ZS” and “Xu Ze-shui”. After processing the data, the research results can reflect the real situation more accurately. As reflected by Fig. 4, the core of the study on IFS was dominated by distinguished scholars. The top authors in the IFS studies based on frequency are presented in Table 5. Atanassov KT is a Professor from Bulgarian Academy of Sciences. Professor Atanassov is the founder of IFS theory and he contributed a lot of fundamental research results which are very important for development of this theory. Professor Zadeh LA is a professor from the University of California. Meanwhile, he is a mathematician, electrical engineer, computer scientist. Since IFS is the generalization of FS, the FS theory is certainly very critical for the development of IFS theory. Xu ZS is the Professor at Sichuan University, China. As an expert in information fusion, group decision making and fuzzy sets, Professor Xu has authored more than 400 journal articles to professional journals and served on editorial boards of some renowned academic journals.
As the same situation of Fig. 3, most authors with great influences in this field were in earlier years. There is no core authors emerged even if the number of researchers who focused on the area of IFS theory increased every year (Fig. 5).
Influential journals
By some accounts, there are hundreds of journals publishing articles related to IFS theory. The main journal clusters are shown in Fig. 6. The top 10 journals in IFS area according to frequency were shown in Table 6 in detail. From Fig. 6 and Table 6, we found that Fuzzy Sets and Systems, Information Sciences, Information Control, IEEE Transactions on Fuzzy Systems, and Expert Systems with Applications are the top influential journals in the research of IFS area.
Research findings and conclusions
According to the detailed analysis of the above sections, some useful and interesting research findings can be yielded:
First, the reference [2] plays a crucial role in the development of IFS theory although the concept of IFS theory was put forwarded by Atanassov [1].
Second, some fundamental researches were received in 1980s–1990s.
Third, the core of the IFS study was dominated by distinguished scholars. Atanassov KT (Bulgarian Academy of Sciences, Bulgaria), Zadeh LA (University of California, Berkeley, USA), Xu ZS (Sichuan University, China), Szmidt E (Polish Academy of Sciences, Poland) and Bustince H (Public University of Navarra, Spain) are main contributors for the development of IFS studies.
Fourth, the journals such as Fuzzy Sets and Systems, Information Sciences, Information Control, IEEE Transactions on Fuzzy Systems and Expert Systems with Applications are the top influential journals in IFS studies.
This paper have made a scientometric review on IFS study to reveal the most cited paper, the influential authors and the influential journals in IFS domain based on the 1318 references. The most cited paper, the influential authors and the influential journals in this domain have been revealed in this paper. The research findings of this paper are based on the objective data analysis and they are less affected by subjective biases which make them more reliable.
Footnotes
Acknowledgments
This work has been supported by the Philosophy and Social Sciences Planning in Zhejiang Province (16NDJC159YB), the National Natural Science Foundation of China (No. 71301142, No. 71501135), the National Education Information Technology Research (No. 146242069), the Fundamental Research Funds for the Central Universities (No. skqy201649), and the Scientific Research Foundation for Scholars at Sichuan University (No. 1082204112042).