A Bibliometric Review of Type-3 Fuzzy Logic Applications

Abstract

In this paper, we provide an overview of type-3 fuzzy logic systems (T3FLSs) and their applications in a general way. The contribution of this paper is to analyze and review, in the best way possible, applications in several fields utilizing type-3 fuzzy logic systems. Recently, many algorithms are receiving more and more attention in this area, and for this reason, an overview of this field is important. This article provides an overview of the most important applications in which intelligent computing methods based on T3FLSs are used. The main goal of this paper is to thoroughly explore these applications and identify emerging scientific trends in the adoption of intelligent methods, particularly those involving T3FLSs. To achieve this, we use the VosViewer software to construct and visualize bibliometric networks. VosViewer is a free, Java-based tool designed for analyzing and visualizing bibliometric data. This program is used for the creation of maps of papers, authors, etc., and the development of maps for keywords, countries, research groups, and more.

1. Introduction

Nowadays, the use of systems based on computational intelligence and fuzzy logic systems to enhance the performance and obtained results achieved with traditional techniques for applications in many areas is becoming very popular. Therefore, we analyze several applications in this area, specifically those of T3FLSs. In this approach, we use VosViewer software version 1.6.20 [1,2] to review the most relevant papers in the analyzed applications, authors, dates, citations, networks, clusters, and important information for every case studied. Most of the information presented here was collected from the Scopus database. The main reason for using Scopus is that this database contains most of the indexed publications. However, we also performed a query on the Web of Science database to observe only the indexed journals in the journal citation report (JCR). Recently, there has been an important interest in T3FLSs for solving complex problems. The main idea is to review the most important applications using this type of fuzzy logic and the application areas. The objective of this study was to highlight the importance that T3FLSs have as a good alternative with respect to type-1 and type-2 fuzzy logic systems. One motivation for this study was to perform an analysis and to appreciate the different ways in which the artificial techniques considered in this survey are being used to develop new applications to solve problems using fuzzy rules. The contribution of this paper is a review about the authors, countries, works, etc., in the area of type-3 fuzzy logic. With the collected information, we can build relationships and networks to appreciate the presented works in the best way, which give an idea of the state of the art and also help to envision future trends in this area. The novelty of this paper is mainly reflected by the fact that there is currently no review of this kind on T3FLSs in the state of the art, so an overview of this area is presented for the first time in this paper. This paper is structured as follows. In Section 2, a summary about T3FLSs is presented, and Section 3 offers a the literature review in general form of the utilization of T3FLSs in different applications. In Section 4, the results and analysis of some queries performed in this work from the Scopus database and the bibliometric Vosviewer software are presented. Section 5 outlines future trends for T3FLSs. The conclusions of our analysis are presented in the last section.

2. A Brief Description of Type-3 Fuzzy Logic Systems

Interval type-3 fuzzy logic (IT3FL) was postulated as an extension of type-2 fuzzy logic, and a brief description of type-3 fuzzy sets is presented to appreciate how they differ from type-2 fuzzy sets. Since the emergence of fuzzy sets, proposed by Zadeh [3], these kinds of sets have evolved for handling more information, starting from vagueness to a high level of uncertainty. This section summarizes the differences between these variations of fuzzy sets. The general definitions of type-1, type-2, and type-3 fuzzy sets are expressed in a succinct way in (1), (2), and (3), respectively.

$$\begin{array}{c}{A}^{\left(1\right)}=\left\{(x,{\mu }_A\left(x\right))\right|\forall x\in [0,1]\}\hfill \end{array}$$

(1)

$$\begin{array}{c}{A}^{\left(2\right)}=\{\left(\left(x,u\right),{\mu }_{\tilde{A}}\left(x,u\right)\right|\forall u\in J_x\subseteq [0,1]\}\hfill \end{array}$$

(2)

$$\begin{array}{c}{A}^{\left(3\right)}=\{\left(\left(x,u\right),{\mu }_{A^{\left(3\right)}}\left(x,u,v\right)\right|x\in X,u\in U\subseteq [0,1],v\in V\subseteq [0,1]\}\hfill \end{array}$$

(3)

These approaches are called generalized fuzzy sets, and as can be seen, with the progression of the fuzzy sets, the definitions are more complex, handling vagueness, uncertainty, and second-order uncertainty, respectively.

Type-3 fuzzy sets [4,5,6,7,8,9], defined by $A^{\left(3\right)}$, are represented by the graph of a trivariate function, named the membership function (MF) of $A^{\left(3\right)}$, in the Cartesian product $\mathit{X}\times \left[0,1\right]\times \left[0,1\right]\mathrm{in}\left[0,1\right]$, $\mathrm{where}\mathit{X}\times \left[0,1\right]\times \left[0,1\right]\mathrm{in}\left[0,1\right]$${\mu }_{A^{\left(3\right)}}$ is defined by ${\mu }_{A^{\left(3\right)}}$$(x,u,v)$ (or ${\mu }_{A^{\left(3\right)}}$ for short) and its named a type-3 MF of the type-3 fuzzy set

$$\begin{array}{c}{\mu }_{A^{\left(3\right)}}:\mathit{X}\times \left[0,1\right]\times \left[0,1\right]\to \left[0,1\right]\hfill \\ A^{\left(3\right)}=\left\{(x,u\left(x\right),v(x,u),{\mu }_{A^{\left(3\right)}}(x,u,v))|x\in \mathit{X},u\in U\subseteq \left[0,1\right],v\in V\subseteq \left[0,1\right]\right\}\hfill \end{array}$$

(4)

where U is the universe for the secondary variable, $u,$ and V is the universe for the tertiary variable, v. If the tertiary MF is uniformly equal to 1, then we have an interval type-3 fuzzy set (IT3FS) with an interval type-3 MF. Figure 1 shows an IT3FS with an interval type-3 MF. $\tilde{\mu }(x,v)$, where $\underline{\mu }(x,v)$, is the lower membership function, and $\overline{\mu }(x,v)$ is the upper MF.

3. Literature Review

This section presents some important works using the T3FLSs reviewed in this work. Today, we observe the technological advancement in fuzzy logic systems, which, as a result, manage uncertainty in the best way possible by improving the results offered by type-1 and type-2 fuzzy logic systems. Fuzzy logic offers techniques that have attracted great interest and that can be used to improve the results of existing applications with traditional methods by providing the capability to handle uncertainty. Recently, it has become more common to observe systems designed with if then rules to help the user solve a specific problem in the best possible way. For this reason, we study fuzzy logic applications using T3FLSs to clearly appreciate the works developed with these types of systems. In [10], a multicriteria fuzzy decision-making method is presented for the selection of manufacturing strategies. In this research, the authors present a further step by introducing the concept of fuzzy set theory in the battle to overcome precision-based evaluation. In addition, in [11], a fuzzy Bayesian-based bow tie risk assessment of runway overrun is presented. On the other hand, in [12], an implementation of biometric identity-based encryption is shown. In [13], a directed Laplacian for the fuzzy autocatalytic set of a type-3 fuzzy graph of an incineration process was presented. In this work, a type-3 fuzzy graph was used in the modeling of clinical waste incineration. In addition, in [14], a coordinated transformation was presented for type-3 fuzzy graphs. An interesting and recent work was presented in [15], where the authors introduced a new data-driven control system for memss gyroscopes using type-3 fuzzy systems. In addition, in [16], an implementation of a deep learning frequency regulation system was described. The controller was designed with a dynamic estimation model, error feedback controller, and interval compensator type-3 fuzzy logic. In addition, in [17], a methodology was presented for building IT3FLs. In this work, the authors performed a deep analysis of T3FLSs. In [4], an extended study on the IT3FLSs is presented with the theory and design of these fuzzy logic systems. Finally, other important works on fuzzy logic systems contained in Scopus can be found in [18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49].

4. Applications of Type-3 Fuzzy Logic Systems

In this section, we summarize the information collected after reviewing the Scopus database.

4.1. T3FLSs

Many intelligent and fuzzy logic systems have been developed in recent years, with the aim of obtaining the best possible results in several problems. As can be seen in

Table 1. Years, applications, and references of type-3 fuzzy research.

Year	Applications	References
2025	Control systems	[51]
2024	Chaotic systems	[52]
2023	Control systems	[53,54,55,56,57,58,59]
	Forecasting	[5]
	Robotic	[60]
2022	Control systems	[61,62,63,64,65,66,67]
	Time series prediction	[7,68,69,70]
	Image quality	[71]
	Financial forecasting	[72]
	Robotic	[73,74,75]
	Other applications	[6,76,77,78,79,80,81,82,83,84,85,86,87,88,89]
2021	Control systems	[8,90,91]
	Deep learning	[92]
	Several applications	[93,94,95,96]
2020	Hybrid systems	[97]
	Learning algorithm/control systems	[9,98]
2017	Clustering/transportation problems	[99,100]
2016	Transportation problems	[100]
2010	Neural networks	[22]

, a wide range of research has been conducted in many areas. In this case, we are analyzing the most recent applications using type-3 fuzzy logic systems. From the Scopus database, the publications presented in Table 1 were collected. We can observe how many recent works have been published in recent years. To build Table 1, we carefully selected the query ‘Type-3 fuzzy systems’ to find articles in this review in the best way possible. With this query, the total number of documents found by the system was 794. However, not all works described or used T3FLSs; in total, 19 papers were discarded because the search engine found some papers related to other areas, for example, type 2 diabetes, etc. For this reason, as shown in Figure 2, the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) [50] guidelines were taken as a reference for the query described above to clearly analyze the total number of records found in Scopus.

4.2. Search from Scopus

This section outlines some of the queries used to search the Scopus repository to perform a review of the articles with more detail for the selected topics in Table 1. In total, 108 publications from the Scopus database were obtained for the query with the topic ‘type-3 fuzzy logic system’. In addition, in Figure 3, the publications from 2002 to 2025 are presented. In Figure 3, it can be noticed how the number of works has recently increased.

Figure 4 shows the network with strength links and occurrences, with the queries used to find the information from Scopus. The data were collected in plain text and converted to a csv file. Subsequently, the file was introduced into the Vosviewer software to obtain Figure 4. In addition, Figure 5 shows, in the best way, the density of the clusters, where the different research groups working with T3FLSs are appreciated. In Figure 6, the authors with the highest number of publications are highlighted, based on the network built in Figure 5 and the relationship between the authors and their work. Figure 5 emphasizes the most frequently cited authors, highlighting their prominence and influence in the study’s context, showcasing key contributions and geographical regions that significantly impact this research. The settings for finding the information for the queries presented in this section were as follows for all studied cases:

Analysis: Co-authorship (Co-a) and authors.

The minimum number of citations considered for an author in Figure 4 and Figure 5 was 1. Of the 182 authors, 182 met the threshold. For each of the 182 authors, the total strength of the Co-a links with other authors was calculated. Finally, the authors with the greatest total link strength (TLiSt) were considered for the analysis. The attributes of an article are connected to each other through the article itself (for example, author(s) to the journal, etc.). These connections of different attributes can be represented through an article × attribute matrix.

In addition, we queried Scopus to observe the number of publications by authors. From

Table 2. Authors, publications, and countries of type-3 fuzzy logic systems.

Authors	Publications	Countries
Mohammadzadeh, A	44	China
Castillo, O.	36	Mexico
Melin, P.	31	Mexico
Castro J.R.	12	Mexico
Taghavifar, H.	7	Canada
Alattas, K.A.	7	Saudi Arabia
Tarafdar, A.	6	India
Majumber, P.	6	India
Bera, U.K.	6	India
Mosavi A	5	Iran

and Figure 3, we can observe that the number of papers has been increasing in recent years. We can appreciate the top 10 ranking considering the number of papers related to IT3FLSs.

Also, in Figure 7, the network, the strength links, and the countries are shown with the queries used to obtain the information from Scopus. In Figure 7, the countries with the highest number of citations and publications are highlighted, where it can be seen that China, Iran, Saudi Arabia, and Hungary are the five countries that have the highest number of citations according to this study. In fact, Mexico can be highlighted for having many articles. However, the ranking was performed by taking the total strength of the link as a reference. In

Table 3. Country, papers, and citations of type-3 fuzzy logic systems.

Country	Papers	Citations	TLiSt
China	39	767	102
Iran	22	749	71
Taiwan	10	496	56
Saudi Arabia	15	475	52
Hungary	5	362	31
Palestine	4	224	28
South Korea	11	181	26
Vietnam	5	310	25
Turkey	11	100	23
Canada	10	45	22
Mexico	40	544	20
India	12	338	19
Germany	3	256	18
Thailand	3	112	16
Norway	2	155	16
Slovakia	2	62	14
Azerbaijan	5	32	13
Italy	5	22	13
Poland	3	72	12
United Kingdom	3	67	12
Yemen	3	176	12

, the top 20 countries ranked according to the total strength of the link are shown. However, we can also find the number of papers and citations to find more details about each one. The settings used to represent the information of the queries presented in this section were as follows for all studied cases:

Analysis: Co-a and countries.

For each of the 36 countries, the total strength of the Co-a links with other countries was computed. The countries with the highest values were considered.

4.3. Search from Web of Science

This section outlines a study of some queries used to search the Web of Science (WoS) database repository to perform a review of the indexed articles with more detail on the selected topics listed in

Table 4. Authors, papers, and citations of type-3 fuzzy logic systems from the WoS (2019–2025).

Citations
Authors	2019	2020	2021	2022	2023	2024	2025	Avg. per Year	Total
	4	9	84	287	475	600	18	74.75	1495
Mohammad- zadeh, A. et al. [9]	1	4	28	32	29	35	0	21.5	129
Liu, Z. et al. [101]	0	0	8	39	26	22	0	19	95
Mohammad- zadeh, A. et al. [8]	0	0	6	38	28	9	0	16.2	81
Qasem, N. et al. [94]	0	0	6	31	22	14	1	14.8	74
Cao, Y. et al. [92]	0	0	1	30	21	16	0	13.6	68
Taghieh, A. et al. [64]	0	0	0	0	42	21	1	16	64
Mosavi, A. et al. [98]	0	2	9	19	12	2	0	7.33	44
Taghieh, A. et al. [65]	0	0	0	0	25	13	1	9.75	39
Wang, JH. et al. [96]	0	0	0	8	12	18	0	7.6	38
Nabipour, N. et al. [97]	0	0	7	6	13	12	0	6.33	38
Vafaie, RH. et al. [95]	0	0	4	6	18	8	1	7.4	37
Singh, DJ. et al. [87]	0	0	0	4	9	17	0	7.5	30
Ma, C. et al. [6]	0	0	5	8	10	5	0	4.67	28
Castillo, O. et al. [5]	0	0	0	0	10	16	1	6.75	27
Melin, P. et al. [7]	0	0	0	2	16	8	1	6.75	27

. We collected data from the WoS with the same topic as in the Scopus database: ‘type-3 fuzzy logic system’. This study aimed to observe only journals, citations, highly cited papers, etc. In total, 95 articles were obtained from the WoS database for the query with this topic. In addition, in Figure 8, publications from 2005 to 2025 are presented. In Figure 8, it can be observed how the number of papers from the WoS have recently increased. In addition, it is important to note that according to the WoS, from September to October 2024, reference [7] was the most highly cited because it received enough citations to place it in the top 1% of the academic field of mathematics based on a highly cited threshold for the field and publication year. In Figure 9, the cluster generated in Vosviewer with the extracted data from the WoS can be observed. The figure shows the relationships of the main authors working with the analyzed topic. We can notice how the top 15 of the most cited journal papers presented in Table 4 correspond to this figure.

5. Analysis and Future Trends

In this section, we briefly summarize the analysis of the data obtained mainly from Scopus, and also, we envision possible future trends of development for the type-3 fuzzy logic area. Based on the publications that have been published, at the moment, we can say that most type-3 fuzzy papers have been applied in the control area, followed by time series prediction and decision making. However, we expect that other important application areas will be considered in the near future, such as pattern recognition, clustering, and intelligent agents (just to mention a few). In addition, on the theoretical side, at the moment, most papers deal with interval type-3 fuzzy logic (meaning that the tertiary membership function is fixed to a value of one), but we expect that general type-3 logic will usable in the near future, allowing for even better results to be achieved in many complex problems. Of course, for this to be possible, some theoretical achievement would be needed, like better (faster) type reduction methods and possibly other ways to reduce the number of inferences needed, like through the use of shadow sets. Finally, there is also possible theoretical work to be carried out on general type-n fuzzy logic, with this generalizing the form of the fuzzy sets even more, which could also allow for even more interesting theoretical and practical results in the future.

6. Conclusions

After performing an exhaustive analysis of the extracted information from the Scopus database and carrying out a detailed study of the works and relevance of utilizing IT3FLSs, we arrived to the conclusion that this area has achieved remarkable advancement in recent years. We can appreciate the increase in the number of works, citations, countries, authors, and relationships. For example, in the studied references, the inclination has been to develop more works based on the field of T3FL. Also, we have built networks, clusters, and relationships around the world for the researchers working in this area. However, the generated networks in the presented study show that applications such as control, forecasting, robotics, deep learning, and other applications, such as financial forecasting, have been developed with type-3 fuzzy sets. In addition, there are research trends in image quality applications utilizing T3FLSs. Finally, we observed with this analysis that most of the works found using type-3 fuzzy systems were in the control area. There are several limitations for this paper; we can state that this study was mainly based only on the Scopus database, which is not the only existing repository of documents, but it is the largest existing dataset. Other sources, such as Web of Science and Google Scholar, could be used to complement this study. Another limitation is that possible topics (with a small number of documents) may have not been considered. However, we believe that this study is representative of the state of the art in T3FL. In future work, other topics from other databases can be reviewed with this type of software to compare the number of works or relevance considering other sources. In addition, specific queries with other bibliometric software, such as CiteSpace, which is a free software used to visualize and analyze trends and patterns in the scientific literature, can be used to carry out this type of work. The importance of this study is that with this work, readers can appreciate the trends in using T3FLSs in many applications, specifically in the control area. However, this work can also be useful as a reference for building other types of queries, with other keywords or information from different databases. In addition, the same queries can be explored to view updated information on the topics analyzed in this study. Although we only presented the collected information on T3FLSs in this the paper, this paper can be extended to other areas in extensions of fuzzy logic, such as intuitionistic, hesitant, and other types of logic.