Exploring Grey Systems in Uncertain Environments: A Bibliometric Analysis of Global Contributions and Research Themes

Abstract

Grey systems theory, through the special mathematics and methods offered, such as through seeing numbers as intervals rather than fixed values, provides a bridge between the two extreme cases in which a system under investigation might find, namely, a white system, easy to read and understand, and a black system, completely unknown to the investigator. Since its appearance in 1982, the theory has contributed to solving various challenges traditionally addressed through complex means. The paper provides a comprehensive perspective on the evolution of the grey systems domain over the 42-year period analysed, spanning from 1982 to 2024. Utilizing a dataset extracted from the Clarivate Analytics’ Web of Science Core Collection database, the paper conducts a bibliometric analysis that includes the identification of key journals, affiliations, authors, and countries, as well as the collaboration networks among authors and countries. It also analyses the most frequently used keywords and authors’ keywords. The annual growth rate of 12.99% indicates a sustained interest among researchers. Using the Biblioshiny 4.2.3 library in R version 4.4.1, a variety of visualisations have been created, including thematic maps and WordClouds. A detailed review of the most cited papers has been performed to highlight the role of grey systems in advancing intelligent decision-making techniques. In terms of results, it has been observed that the university with the highest contribution to the field is the Nanjing University of Aeronautics and Astronautics while the most influential figure in the area of grey systems in terms of the number of published papers is Sifeng Liu. As expected, China, the home of grey systems theory, is the country with the most notable contribution in terms of published papers and international collaboration networks.

1. Introduction

Grey systems theory was founded in March 1982, when Professor Deng Ju-Long published the article called “Control Problems of Grey Systems”. In this paper, Professor Deng presented the main concepts of “Grey systems” and the “Grey matrix”, together with stability and controllability elements [1]. Furthermore, in the paper, Professor Deng explained, in simple terms, the concept behind the grey system as a system that contains, at the same time, known and unknown information as grey systems derive from the black box concept. In the black box concept, the objects are divided into two different parts: the objects are called “black” if the information is completely unknown while the objects are “white” when the information is completely known.

Liu et al. [2] consider that grey systems theory made significant progress and that it became a more and more interesting topic for researchers. Grey numbers, equations, matrices, and systems represent the foundation of the grey domain. Grey decision-making methods focus on multi-attribute weighted grey target models or grey situation decisions. The actual scientific studies on this topic have been applied to numerous areas such as the social sciences, engineering, the natural sciences, aviation, petroleum, energy resources, transportation, architecture, behavioural science, management, education, law, and military science.

On the other hand, the implementation of sustainability measures is a growing field considering the global economic system at all levels. To ensure balanced and proper implementation, researchers use decision-making procedures to choose the best methodology for possible scenarios. This practice has been reinforced by the EU’s agenda for the implementation of sustainability measures [3], which has laid out the targets to be met by 2030 in accordance with a series of recommendations aimed at promoting not only sustainability but also economic development and living standards. In such circumstances, the use of decision-making procedures becomes increasingly important in integrating economic requirements with long-term sustainable goals. A broad spectrum of alternatives has been covered in the specialized literature; however, grey systems theory outperforms the other methods by incorporating uncertainty factors, which most traditional methods do not consider. The uncertain environment is intrinsically connected to grey systems theory as the distinguishing element of this methodology is the incomplete information underlying uncertain settings [4].

In this regard, Su et al. [5] established a favourable relationship between the integration of grey-systems-theory-specific methodologies and the improvement of sustainability metrics such as material waste reduction. The analysis was conducted in the field of sustainable supply chain management (SSCM), which has received greater attention in the context of sustainability, particularly given the supply chain’s significant contribution to global pollution. Therefore, in this instance, the beneficial impact of grey systems theory methods is highlighted in correspondence with the implementation of sustainability measures.

The purpose of the analysis is to investigate and understand the benefits of grey systems theory implementation in various areas and how the domain evolved during the timespan. In order to achieve the scope, a series of scientific questions have been included as the research will focus on identifying the answers to the following:

• SQ1: What are the main topics discussed in grey systems theory scientific articles?
• SQ2: Which are the most representative universities that contribute to the evolution of the domain?
• SQ3: How is the collaboration network between authors?
• SQ4: Who are the main authors that publish articles related to grey systems theory?
• SQ5: Which are the journals with the highest numbers of publications?
• SQ6: Which countries have the most publications and citations?

The article is divided into five parts as follows: the initial part explores the introductory elements and concepts of grey systems theory, together with the scope of the research. The second section explores the methods used in the bibliometric approach, explaining, also, the main steps of extracting the database from the ISI Web of Science database. The third section investigates the dataset from different perspectives, extracting the major keywords, authors, universities, journals, and sources and focusing on the five most cited global documents, thematic map evolution, factorial analysis, and WordClouds. The fourth section describes the discussions and limitations of the paper, and the last section includes the concluding remarks.

2. Materials and Methods

Taking into consideration the existing articles, Clarivate Analytics’ Web of Science Core Collection [6], known as Web of Science or WoS, was selected for the bibliometric research. Shamsi et al. [7] justify the choice for the Web of Science database as being one of the most reliable publisher-independent global citation databases in the world. Furthermore, in terms of citations, Gerasimov et al. [8] have compared the citation coverages in various databases such as Google Scholar, Web of Science, Scopus, Crossref, and DataCite. The authors have highlighted that while, until 2020, Scopus outperformed Web of Science, starting with this date, the Web of Science database has provided a superior performance. Various issues related to the use of WoS database as a base for bibliometric studies have been further discussed in the scientific literature, such as, but not limited to, the use of H index [9], search using the Digital Object Identifier (DOI) [10], DOI errors and possible solutions to solve the situation [11], publication date issues [12], and historical data retrieval [13], showing once more the interest of the scientific community in the use of this database from bibliometric analysis purposes.

The purpose of the research is to evaluate the academic community on the topic of the grey system in uncertainty environments, extracting the main affiliations, journals, authors, countries, evolution of publications, numbers of citations, numbers of keywords, most representative bigrams and trigrams, and thematic map evolution or what themes have been studied in the 10 most cited documents using a bibliometric approach. The bibliometric method highlights the major structural elements of the analysed topic on the entire timespan that has been included, presenting the evolution of the domain that begins as a theoretical subject and evolves into a practical domain with a variety of applications in business, sustainability, or medicine [14,15,16].

A crucial step when a bibliometric analysis is performed with WoS database is to detail the indexes that have been used on the data extraction step, as Liu presented [17,18]. The indexes that are included could affect the number of documents that are extracted since WoS offers numerous paid subscriptions. In this case, the Clarivate Analytics’ Web of Science Core Collection indexes that were included into research were the following:

• Index Chemicus (IC)—2010–present;
• Conference Proceedings Citation Index—Social Sciences and Humanities (CPCI-SSH)—1990–present;
• Emerging Sources Citations Index (ESCI) 2005–present;
• Science Citation Index Expanded (SCIE)—1900–present;
• Book Citation Index—Science (BKCI-S)—2010–present;
• Current Chemical Reactions (CCR-Expanded))—2010–present;
• Book Citation Index—Social Sciences and Humanities (BKCI-SSH)—2010–present;
• Social Sciences Citation Index (SSCI)—1975–present;
• Conference Proceedings Citation Index—Science (CPCI-S)—1990–present;
• Arts and Humanities Citation Index (A&HCI)—1975–present.

Figure 1 includes the main steps that are required in order to perform a bibliometric analysis according to Cobo et al. [19] and Zupic and Cater [20]. The first step is the data extraction based on keywords that are related to the topic: here, grey systems theory. The next step is to investigate the extracted dataset from different points of view: sources, authors, countries, most cited documents, and mixed analysis [21,22,23,24,25,26]. Based on the results, the discussion, limitations, and conclusions are elaborated.

Table 1. Data selection steps.

Exploration Steps	Questions on Web of Science	Description	Query	Query Number	Count
1	Title	Contains one of the grey-systems-specific keywords a	(((((((((TI=(“grey_system*”)) OR TI=(“grey_number*”)) OR TI=(“grey_cluster*”)) OR TI=(“grey_control*”)) OR TI=(“grey_decision*”)) OR TI=(“grey_incidence*”)) OR TI=(“grey_model*”)) OR TI=(“grey_theor*”)) OR TI=(“grey_sequence*”)) OR TI=(“grey_prediction*”)	#1	3011
		Contains one of the grey-systems-specific keywords b	(((((((((TI=(“gray_system*”)) OR TI=(“gray_number*”)) OR TI=(“gray_cluster*”)) OR TI=(“gray_control*”)) OR TI=(“gray_decision*”)) OR TI=(“gray_incidence*”)) OR TI=(“gray_model*”)) OR TI=(“gray_theor*”)) OR TI=(“gray_sequence*”)) OR TI=(“gray_prediction*”)	#2	476
2	Abstract	Contains one of the grey-systems-specific keywords a	(((((((((AB=(“grey_system*”)) OR AB=(“grey_number*”)) OR AB=(“grey_cluster*”)) OR AB=(“grey_control*”)) OR AB=(“grey_decision*”)) OR AB=(“grey_incidence*”)) OR AB=(“grey_model*”)) OR AB=(“grey_theor*”)) OR AB=(“grey_sequence*”)) OR AB=(“grey_prediction*”)	#3	6585
		Contains one of the grey-systems-specific keywords b	(((((((((AB=(“gray_system*”)) OR AB=(“gray_number*”)) OR AB=(“gray_cluster*”)) OR AB=(“gray_control*”)) OR AB=(“gray_decision*”)) OR AB=(“gray_incidence*”)) OR AB=(“gray_model*”)) OR AB=(“gray_theor*”)) OR AB=(“gray_sequence*”)) OR AB=(“gray_prediction*”)	#4	2193
3	Keywords	Contains one of the grey-systems-specific keywords a	(((((((((AK=(“grey_system*”)) OR AK=(“grey_number*”)) OR AK=(“grey_cluster*”)) OR AK=(“grey_control*”)) OR AK=(“grey_decision*”)) OR AK=(“grey_incidence*”)) OR AK=(“grey_model*”)) OR AK=(“grey_theor*”)) OR AK=(“grey_sequence*”)) OR AK=(“grey_prediction*”)	#5	4407
		Contains one of the grey-systems-specific keywords b	(((((((((AK=(“gray_system*”)) OR AK=(“gray_number*”)) OR AK=(“gray_cluster*”)) OR AK=(“gray_control*”)) OR AK=(“gray_decision*”)) OR AK=(“gray_incidence*”)) OR AK=(“gray_model*”)) OR AK=(“gray_theor*”)) OR AK=(“gray_sequence*”)) OR AK=(“gray_prediction*”)	#6	762
4	Title/Abstract/Keywords	Contains one of the grey-systems-specific keywords	#1 OR #2 OR #3 OR #4 OR #5 OR #6	#7	9977
5	Language	Limited to English written papers	(#7) AND LA=(English)	#8	9781
6	Selecting the papers related to grey theory	Limited to grey theory	Manually selected papers	#9	9169

^a “grey” terms are considered; ^b “gray” terms are considered.

presents the main steps that have been applied in order to extract the database. The first step filtered the titles by looking for a group of words: “grey_system*”, “grey_number*”, “grey_cluster*”, “grey_control*”, “grey_decision*”, “grey_incidence*”, “grey_model”, “grey_theor*”, “grey_sequence*”, and “grey_prediction*”, resulting in 3011 documents, or “gray_system*”, “gray_number*”, “gray_cluster*”, “gray_control*”, “gray_decision*”, “gray_incidence*”, “gray_model”, “gray_theor*”, “gray_sequence*”, and “gray_prediction*”, resulting in 476 documents. The use of “*” replaces one or more letters in order to find the singular or plural form of each word. The use of “*” also includes the situation in which no additional character is added to the word where it is used—e.g., the use of “grey_cluster*” form returns the papers that contain either “grey cluster” or “grey clustering” as a group within the category of search (title/abstract/authors’ keywords).

The second step filtered the abstracts using the same keywords described above, obtaining 6585 documents for the filters that contain “grey” while for the filters that contained “gray”, there were 2193 publications. The keywords that were utilized for filtering the ISI Web of Science database were in line with similar bibliometric analysis that explored the evolution of grey systems in economics and education [27], the evolution of grey systems between 1996 and 2010 [4], or the major trends in grey systems theory area between 1991 and 2018 [28].

The third step was looking at the keyword level and using the same list of search terms; a total of 4407 papers were extracted by using the words that contained “grey” and 762 documents by using the words that contained “gray”. Similar documents used the mentioned keywords that were related to grey systems domain, which explores the evolution of grey systems and the impact in economic and education [4,27,28].

The fourth step included, in the database, only the documents that were part of the first three steps, resulting in a total of 9977 papers.

The fifth step limited the publications by only including the documents that had been published in English, reducing the size of the dataset to 9781 articles. According to Thangavel and Chandra [29], analysing papers that have been written exclusively in English offers consistency and accessibility in bibliometric research. If more than one language has been included in analysis, a mislead on the n-grams, keywords, and themes analysis could be registered, affecting the outcome. Similar bibliometric papers have eliminated other languages apart from English: for example, those that investigated Artificial Intelligence and Machine Learning [16] or energy communities [27].

The last filter excluded the articles that focused on “Bragg-Gray”, “Fine-Gray”, and “Fine and Gray” theory, which had been included in first steps as a result of the used keywords, as these theories were not related to grey systems theory. The final dataset was reduced to 9169 papers, which will be analysed from a bibliometric point of view.

In this case, there was no filter on the type of paper, with the dataset including articles, books, chapters, reviews, scripts, and many other categories. The date on which the dataset was retrieved was 7 September 2024.

3. Dataset Exploration

The third section investigates the extracted dataset from different perspectives, pointing out the main sources, authors, countries, keywords, thematic evolution, collaboration network, and which are the five most globally cited documents.

3.1. Dataset Presentation

The initial part of the third section explores the dataset by extracting information on variables such as the timespan, number of documents, sources, references, average years from publication, number of authors, Keywords Plus, authors’ keywords, which types of documents have been included in analysis, annual scientific production, and average citations per year.

Table 2. Main information.

Indicator	Value
Timespan	1982:2024
Sources	3483
Documents	9169
Average years from publication	9.1
Average citations per documents	12.15
References	158,021

investigate the data by extracting the main information. The period analysed began in 1982 and ended in 2024, representing 42 years, which included 3483 sources, 9169 documents, and 158,021 references. The average number of years taken for publication was 9.1 and the average number of citations per document was 12.15. Compared to similar scientific papers, the number, 9169 documents, was much higher. Pan et al. [28] investigated 4859 documents that had been published between 1991 and 2018 while Prakash et al. [30] evaluated a total of 392 documents that had been published between 2011 and 2021. The article with the closest number of papers was published by Fang et al. [31] and explored a total of 8898 articles that had been released between 2010 and 2020. Prakash et al. [30] discovered an average years from publications of 4.52 years, with a mean number of citations per document of 3.591 and a total of 5084 references, while Fang et al. [31] presented the average citation rate per field: Management had an average citation rate of 33.89, Business 30.96, Economics 25.30, and Green and Sustainable Science and Technology 34.35. In our case, the number of papers was higher compared to that in existing articles in the academic community, but this was due to the higher average number of years from publication. The mean number of citations per document was smaller compared to that in Fang et al. [31] due to the fact that the focus of the authors was to evaluate the fields where grey systems had been implemented, but compared to Prakash et al. [30], the mean citation rate was much higher because the top three most cited papers included in our analysis were published in 1982 and 2010, years that have not been included in the analysis.

Table 3. Authors description.

Indicator	Value
Authors	13,232
Authors of single-authored documents	678
Authors of multiple-authored documents	12,554
Co-authors per document	3.29
International co-authorship	11.28%
Authors’ keywords (DE)	18,963
Keywords Plus (ID)	5410

explores the author information. There were over 13,232 authors included in the dataset, which used 18,963 authors’ keywords and 5410 Keywords Plus. There were 12,554 multiple-authored documents and 678 single-authored documents, with an average number of co-authors per document of 3.29 and an international co-authorship of 11.28%. Considering the paper written by Prakash et al. [30], the database that has been analysed by the authors contains a total of 1179 Keywords Plus, 835 authors’ keywords, 623 authors, 11 single-authored papers, 403 multiple-authored documents, and 3.19 co-authors per article. Due to the size difference among the datasets, in order to perform a correct comparison, the single- and multiple-authored documents have been calculated as percentages of the total number of articles. In our case, the single-authored documents represent approximately 7.39% of the total articles compared to the 2.80% in Prakash et al.’s [30] paper, resulting a higher distribution of single-authored documents in our dataset. A similar approach has been applied to the authors’ keywords and Keywords Plus, dividing the number to the number of documents. In our document, the average number of Keywords Plus per document is only 0.59 while the number of authors’ keywords per document is 2.06. Prakash et al. [30] had an average of three Keywords Plus per paper and 1.58 authors’ keywords per document. The difference is significant for Keywords Plus and it can be explained by the limited access to Keywords Plus, authors’ keywords, and abstracts for the articles published before 1990, as Liu et al. [13] explained, which could have affected the outcome since the timespan was between 1982 and 2024.

Table 4. Frequency of document types.

Document Type	Value
Article	5057
Book chapter	36
Letter	5
Proceedings paper	3747
Review	68

focuses on the types of papers that have been included in the dataset. The highest number of papers, 5057, was for “Article”, followed by “Proceedings paper” with 3747. There were only sixty-eight papers marked as “Review”, thirty-six as “book chapter”, and five as “letter”. According to Pan et al. [28], who evaluated the grey systems theory topic, the most common type of document that has been investigated using the bibliometric approach differs from one year to another. Between 2000 and 2016, most of the papers that had been investigated were proceeding papers, followed by articles and a few reviews or retracted publications. In 2017, most papers were articles, representing the single year of the analysed timespan wherein articles were the majority.

Figure 2 explores the yearly scientific production of grey system documents.

The first three articles were published in 1982 and the next one was published in 1986. Starting with 1993, when nine articles were released, the trend started to increase in a positive manner, with twelve articles in 1994 and 1995, and fifteen in 1996, achieving 47 in 2001. The trend growth exponentially in 2004 when, from 64 documents in 2003, it grew to 111 in 2004, achieving a total in 2009 of 467 publications. Between 2012 and 2020, the annual production rate was between 400 and 500, and in 2021, the level rose a little to 579 papers. In 2022, 649 papers were published, representing the peak while, in 2023, there were 563 documents and, in 2024, 420 articles. Prakash et al. [30] evaluated the grey systems theory publications that had been released between 2011 and 2021. The trend of the publications was positive up to 2020, starting with 25 in 2011 and achieving a peak in 2020 with 60 papers published. In 2021, there was a decrease from 60 papers to 31.

Similar results have been observed also by Wani and Ganaie [32], who investigated the same timespan, between 2011 and 2021, and the same topic, grey systems. In 2011, 201 papers were published, and the peak was achieved in 2020, with 606 papers published. In 2021, there was a small decrease, from 606 to 547 articles. In our case, there was also a positive trend during the timespan, having several decreases, but the peak was registered in 2022, followed by a significant decrease, which may be explained by the keywords that were included into the extraction step. The outcomes of our paper and the investigated articles from the academic community follow a similar pattern.

With all this, it shall be mentioned that the increased interest in research in a particular research area might also be affected by the general trend that favourises the scientific publication number, which might be due to a continuous increase in the number of research institutes and researchers that are pursuing research careers, as Ofer et al. [33] and Vincent-Lacrin [34] pointed out in their work. Furthermore, the expansion of the Web of Science Core Collection might have been another cause for the growth in the number of publications [35].

Figure 3 presents the average yearly citations. The highest value was registered at the beginning of the timespan, in 1982, with a value of 25.2 citations per year. The value decreased significantly between 1982 and 1986, achieving an average citation rate of 0.9 in 1986. Until the end of the timespan, the citations values were between 0.5 and 3.5 with small periods of peaks.

3.2. Source Investigation

The focus in the second section is to understand which the most relevant sources are based on Bradford’s Law, the number of documents, and local impact by using the HirscH index.

Figure 4 described the top 10 most relevant sources based on the numbers of publications. In first place, with 468 articles, is Journal of Grey System, followed by Grey Systems: Theory and Application with 250 papers and Expert Systems with Applications with 123 documents. In fourth place is Proceedings of 2007 IEEE International Conference on Grey Systems and Intelligent Services, Vols 1 and 2 with 117 publications while Mathematical Problems in Engineering released 107 articles, Sustainability 105 documents, and Energy 104 articles. The last three journals are Kybernetes, Journal of Cleaner Production, and Applied Mathematical Modelling, which published 90, 80, and 69 documents. Yin [4] explored the grey systems theory domain from a bibliometric point of view between 1996 and 2010, and some of the most relevant journals were Journal of Grey System, Expert System with Applications, Energy, and Applied Mathematical Modelling. Wani and Ganaie [32] evaluated the grey systems theory topic from a bibliometric perspective, discovering that PloS ONE was the most representative journal with 98 articles, followed by BMJ Open with 65 papers, Environmental Evidence with 44 articles, and Sustainability with 37. There were also similar journals with our results, such as Journal of Cleaner Production, Expert Systems with Application, and Grey Systems: Theory and Application, but their impacts were much reduced. It can be stated that there are specific publications where authors publish scientific papers related to the grey systems topic regardless of the topic, but due to the expansion of the domain and limited timespans that have been analysed by other authors, there are journals that have not been included in our top 10.

With regard to the journals listed in Figure 4, a further analysis has been conducted on WoS and the data in

Table 5. Relevant sources based on 2023 WoS Journal Citation Report.

Source	Name of the Publisher	WoS Edition	2023 JIF	JIF Quartile	AIS	AIS Quartile
Journal of Grey System	Research Information	SCIE	1.0	Q4	0.123	Q4
Grey Systems: Theory and Application	Emerald Group	SCIE	3.2	Q1	0.336	Q3
Expert Systems with Applications	Elsevier	SCIE	7.5	Q1	1.330	Q1
Sustainability	MDPI	SCIE, SSCI	3.3	Q2/Q3	0.533	Q3
Energy	Elsevier	SCIE	9.0	Q1	1.328	Q1
Kybernetes	Emerald Group	SCIE	2.5	Q2	0.352	Q3
Journal of Cleaner Production	Elsevier	SCIE	9.8	Q1	1.590	Q1
Applied Mathematical Modelling	Elsevier	SCIE	4.4	Q1	0.897	Q1

have been retrieved. It should be mentioned that in Table 5, only the journals listed in the last WoS report [36] have been provided. As can be observed, the top sources belong mainly to four publishers, namely, Elsevier, Emerald Gorup, MDPI, and Research Information. Most of the sources are indexed in well-quoted journals listed in the first quartiles of the 2023 WoS Journal Citation Report with respect to the journal impact factor (JIF) while having good scores in terms of the article influence score (AIS) values.

Figure 5 contains the most significant journals based on the number of citations, isolating the journals with smaller numbers of citations. Using the Bradford’s Law method, the journals have been separated into three different categories by taking into account the numbers of documents and the rule that each category must contain the same number of documents. In the final step, Bradford’s Law clustered proportionally with 1:n:n² as Yang et al. [37] explained. There are numerous journals that have been included with Bradford’s Law, and the most crucial ones, based on the numbers of papers, are Journal of Grey System with 468 papers, Grey Systems: Theory and Application with 250 documents, Expert Systems with Applications with 123 articles, Proceedings of 2007 IEEE International Conference on Grey Systems and Intelligent Services, Vols 1 and 2 with 117 publications, and Mathematical Problems in Engineering with 107 papers. Delcea et al. [27] evaluated the grey systems theory domain between 1987 and 2021, investigating a total of 1624 documents. On Bradford’s Law, the authors found that Journal of Grey System, Sustainability, Expert System with Applications, Journal of Cleaner Production and Energy were the most representative journals in the analysed area.

Figure 6 details the most relevant local sources based on the value of the H index. The H index is used in order to differentiate local and global citations. Global citations refer to citations that have been obtained from “all over the world” while local citations refer to the number of references obtained from articles included in a collection, as is explained on the Bibliometrix webpage [38]. The H index calculates the total number of papers that have the source cited at least the same number of times [39]. The G index is an improvement of the H index, taking into consideration only unique greatest numbers, wherein the top g papers have received, together, at least g² citations [40].

Based on the H index and G index values, the most significant journal is Energy, which has an H index value of 46 and a G index value of 84, followed by Expert Systems with Applications with an H index of 39 and a G index of 69. In third place is Journal of Cleaner Production with an H index of 38 and a G index of 64, followed by Applied Mathematical Modelling with an H index value of 34 and a G index value of 57. The rest of the journals have smaller impacts but are worthy of being mentioned: Applied Soft Computing (21 H index, 29 G index), Grey Systems: Theory and Application (21 H index, 31 G index), International Journal of Advanced Manufacturing Technology (21 H index, 39 G index), Computers & Industrial Engineering (20 H index, 28 G index), Journal of Grey System (20 H index, 30 G index), and Sustainability (19 H index, 28 G index).

Furthermore, according to the 2023 WoS Journal Citation Report [36], the local sources listed in the top contributors mainly belong to Elsevier, with most of them scoring high JIF values, and most of them are being listed in the top quartile based on JIF values or AIS values—please consider the information in

Table 6. Relevant local sources based on 2023 WoS Journal Citation Report.

Source	Name of the Publisher	WoS Edition	2023 JIF	JIF Quartile	AIS	AIS Quartile
Energy	Elsevier	SCIE	9.0	Q1	1.328	Q1
Expert Systems with Applications	Elsevier	SCIE	7.5	Q1	1.330	Q1
Journal of Cleaner Production	Elsevier	SCIE	9.8	Q1	1.590	Q1
Applied Mathematical Modelling	Elsevier	SCIE	4.4	Q1	0.897	Q1
Applied Soft Computing	Elsevier	SCIE	7.2	Q1	1.282	Q1
Grey Systems: Theory and Application	Emerald Group	SCIE	3.2	Q1	0.336	Q3
International Journal of Advanced Manufacturing Technology	Springer,	SCIE	2.9	Q2	0.493	Q3
Computers & Industrial Engineering	Elsevier	SCIE	6.7	Q1	1.214	Q1
Journal of Grey System	Research Information	SCIE	1.0	Q4	0.123	Q4
Sustainability	MDPI	SCIE, SSCI	3.3	Q2/Q3	0.533	Q3

. As the JIF distribution has been used for comparing different journals across various domains, the importance of the indicator has increased over time [41].

3.3. Authors Investigation

The authors are a crucial part of bibliometric research, and the main authors will be extracted, together with annual production.

Figure 7 describes the most influential authors based on the numbers of published articles. The articles fractionalized express the individual contribution to a specific number of articles that have been published [38].

In first place, with the greatest number of papers, is Liu S. F., with 354 papers and an article fractionalized value of 115.67, the highest among the top 10. In second place is Wang Y. with 119 documents and an article fractionalized value of 31.56, followed by Xie N. M., who released a total of 106 papers and an article fractionalized value of 38.19. Yang Y. H. also published 106 articles, with an article fractionalized value of 31.98, while Zeng B. released a total of 100 publications. The last five authors published fewer than 100 articles: Dang Y. G. (99 papers, 29.55 articles fractionalized), Fang Z. G. (95 papers, 25.00 articles fractionalized), Liu Y. (92 papers, 28.36 articles fractionalized), Li Y. (90 papers, 26.44 articles fractionalized), and Zhang Y. (83 papers, 28.06 articles fractionalized). Similar papers from the academic community have been investigated. Delcea et al. [27] found that Liu S. F. was found as the most representative author based on the number of publications, with a total of 58 papers, while Wang Y. (19 papers), Xie N. M. (17 papers), Liu Y. (20 papers), and Zeng B. (18 papers) have had significant impacts on the grey system topic. Prakash et al. [30] highlights Liu S., Mahmoudi A., Feylizadeh M. R., Javed S. A., and Darvishi D. as the most cited five authors in the grey system field. Pan et al. [28] presented, as the most crucial authors for the grey system field, Liu S. F., Fang Z. G., Wang Y., Zhang Y., Zeng B., Yang Y. J., and Wang J. Compared with our results, there were multiple common authors such as Liu S. F., Wang Y., and Zhang Y., but there were also different authors considered to be the most representative due to multiple factors such as the analysed timespan, and the keywords that had been used for database filtering, resulting in different papers for each research process. Thanks to the development of the topic, more and more authors have started to research and explore grey systems, which has helped in the evolution of the field and to improve the existing methods.

Figure 8 includes the most influential authors based on yearly production. Liu S. F. is the most relevant author, and they released their first papers in 2000, obtaining an average yearly citation rate of 1.44. Starting in 2004, Liu S. F. started to work on papers yearly. In 2010, Liu S. F. published 30 articles, with an average total number of citations per year of 86.73, and the peak was in 2017, with 32 articles and an average total number of citations per year of 61.25. In second place is Wang Y., who published their first article in 2004 and achieved the maximum number of papers published in one year in 2022, with 19 articles, which obtained an average number of citations per year of 76.67. In third place is Xie N. M., who released their first paper in 2005, with an average total number of citations of 0.85. In 2022, 13 publications were released, with an average number of citations per year of 51.67. In fourth place is Yang Y. J., who published their first publication in 2007, which had a very small impact. In 2021, nine papers were published, which obtained a total of 33.17 citations per year. The rest of the authors are also relevant for the research, but their impact was reduced compared with the first four, but they are worth mentioning: Zeng B., Dang Y. G., Fang Z. G., Liu Y., Li Y., and Zhang Y.

3.4. Countries’ Investigation

The most relevant affiliations and countries are extracted based on the numbers of papers and citations. The world collaboration map will be evaluated, extracting the 10 most significant collaborations between countries.

Figure 9 details the 10 most influential affiliations based on the number of publications. In first place, with the greatest number of articles is the Nanjing University of Aeronautics and Astronautics with 821 documents, followed by the Chinese Academy of Sciences and the North China Electric Power University, having 238 and 220, respectively. In fourth place is the Wuhan University of Technology with 216 articles while Assistance Publique Hopitaux Paris (APHP) is fifth with 185 papers. In sixth place is another university from France, Universite Paris Cite with 150 documents, followed by the Hebei University of Engineering and the University of California System with 149 and 142 documents. The last two universities are the University of Toronto and the Nanjing University of Information Science and Technology with 139 and 137 publications. According to Pan et al. [28], the Nanjing University of Aeronautics and Astronautics is the most significant affiliation based on the number of publications, with a total of 434 articles, followed by the North China Electric Power University (166 articles), Wuhan University of Technology (113 articles), and Chinese Academy of Sciences (77 articles). Other relevant affiliations are De Montfort University (42 articles) and the Hebei University of Engineering (40 articles). Prakash et al. [30] extracted the Nanjing University of Aeronautics and Astronautics as the most influential affiliation in the grey system sector with a total of 124 papers, followed, at a difference of 100 papers, by the Henan Agricultural University with only 24 articles, the Nanjing University of Informatic Science and Technology with 22 articles, the Shantou University with 17 documents, and De Montfort University, which published 15 papers. Most of the Nanjing University popularity is thanks to Liu S. F., who published the most articles, and they are one of the most influential authors in the topic of grey systems, with hundreds of articles published. Alongside Liu S. F., there are also numerous important authors who contributed significantly to the evolution of grey systems theory such as Xie NM or Yang Y. J. However, as a consequence of the field’s development, grey systems has now a multitude of applications in numerous industries, which could represent a reason why our research has had different results from the existing academic-community papers regarding the most influential affiliations.

Figure 10 includes the 10 most representative countries based on the total number of SCPs (Single-Country Publications) and MCPs (Multiple-Country Publications). In first place is China, with the greatest number of articles published, having a total of 7487 documents, with 6904 SCPs (92.2%) and 583 MCPs (7.8%). China has a proportion of 81.7% of the total documents published in the grey systems domain, showing the interest and importance of Chinese authors. In second place is India, with 240 documents, with a global contribution of 2.6%, having 211 SCPs (87.9%) and 29 MCP articles (12.1%). In third place is the USA, with 175 publications; 113 documents are SCPs (64.6%) and 62 MCPs (35.4%), representing only 1.9% of the total articles. In fourth and fifth place are Iran and Turkey with 123 and 107 papers. Iran’s contribution is around 1.3% while Turkey’s contribution is approximately 1.2%. Turkey has more SCPs, ninety-eight in total (91.6%), compared to Iran, which has ninety-four papers (76.4%), while Iran has more MCPs, twenty-nine in total (23.6%), compared to Turkey, which has nine (8.4%). In sixth place is the UK, with 84 documents, 44 SCPs (52.4%), and 40 MCPs (47.6%), having the highest percentage of MCPs, indicating the lack of experience for the UK, which has collaborated with international authors more experienced in the grey systems domain, representing 0.9% of the total articles published. Japan is seventh, with 70 documents, having a small contribution of 0.8%, with 54 SCPs (77.1%) and 16 MCPs (22.9%) articles. Poland and Canada are in eighth and ninth places, with 59 and 53 documents, having a contribution of 0.6%. Poland released fifty SCPs (84.7%) and nine MCPs (25%) while Canada published 36 SCPs (67.9%) and 17 MCPs (32.1%). The last country in the top 10 is Romania, with 47 documents published, 33 SCPs (70.2%) and 14 MCPs (29.8%). The contribution of Romania is only 0.5%. According to the academic community, China is the most representative country based on the number of publications, having a total of 1038 papers, followed by India with 357 articles, Turkey with 78, the USA with 63, and Iran with 46 documents [42]. Pan et al. [28] found that China has the highest impact on the grey systems area, with a total of 4433 documents released, followed by the USA with only 146, England with 87, India with 65, Japan with 64, Turkey with 51, Canada with 44, and Iran with 41.

Besides the fact that in the case of grey systems theory, the home country of the theory is China, it should be mentioned that, in general, in the scientific output in the last years, a dominance of Chinese researchers has been observed as acknowledged by the scientific literature. For a comprehensive discussion related to this issue, please consider the recent works from the field of scientometrics [43,44,45].

Figure 11 explores the most cited countries. In first place is China with 74,567 citations and an average article citation rate of 10, followed at a significant difference of 69,705 citations by the USA with only 4862 citations and an average article citation rate of 27.80. In third place is India with 4686 citations, having an average article citation rate of 19.50, followed by Turkey with 3626 citations and an average article citation rate of 33.90. The UK is fifth with 2958 citations and an average article citation rate of 35.20 while Canada has 2342 citations and 44.20 average article citations. The last four countries have less of an impact but are worthy of mentioning: Iran (1699 citations, 13.80 average article citations), Japan (1490 citations, 21.30 average article citations), France (1434 citations, 42.20 average article citations), and Australia (1185 citations, 38.20 average article citations). According to similar papers that have been found in the academic community, Delcea et al. [27] found that China is the most cited country with a total of 26,861 citations, followed by Turkey (2237 citations), India (2205 citations), the USA (2079 citations), Canada (1747 citations), Lithuania (897 citations), Iran (833 citations), Japan (705 citations), Denmark (456 citations), and Australia (437 citations) [27]. Based on Prakash et al.’s [30] results, China has the most number of citations, with a value of five-hundred-and-three, followed by Iran with only eighty-one, India with sixty-four, Turkey with forty-three, Libya with twelve, and the USA with eight citations. Wani and Ganaie [32] explored the grey systems theory literature by using the R programming language and VOSViewer, and according to them, the most impactful country is the USA with 29,830 citations, followed by the UK with 19,810, Canada with 14,090, Australia with 1020, and China with 6335 citations. The results were partially similar in two papers: China was the most representative country, similar to our results, while in the last paper, the USA was the most cited country. India and Turkey appeared as relevant countries in multiple papers, showing the interest of the authors in the grey systems topic. At the same time, there are different results such as those showing the USA in first place, Libya, or the missingness of Denmark or Japan from the top list of the countries.

Figure 12 includes the countries’ collaborations. The most fruitful collaboration was between China and the USA, creating, together, a total of 235 publications, followed by that between China and the UK, with 164 papers.

The next collaborations had smaller numbers of papers but are still worthy of being mentioned: China–Canada with 51 papers, China–Australia with 50 papers, China–Japan with 35 papers, China–Pakistan with 27 papers, the USA–the UK with 27 papers, China–Singapore with 24 papers, China–Korea with 23 papers, and China–Vietnam with 22 papers.

Considering similar works from the field, it has observed that Delcea et al. [27] presents China as the country with the most connections, publishing 67 papers with the USA, 37 with the UK, 19 with Australia and Canada, 14 with Pakistan, and 13 with Iran. Furthermore, Prakash et al. [30] investigated grey systems using a bibliometric analysis. The country with the highest number of publications was China, followed by India, Iran, Turkey or Poland, and Libya. Pan et al. found China, the USA, England, India, Italy, Iran, France, the Netherlands, and Japan as the countries with the highest collaboration between 1991 and 2018, confirming a part of our results. Indeed, China, the USA, the UK, and Japan were identified as the most representative countries in our results, but at the same time, there were different results, such as those with Italy, France, the Netherlands, or Iran, most probably due to the extraction process that included different papers.

3.5. Most Cited Documents Review

This section explores the most relevant documents in the grey systems domain, together with the numbers of authors, regions, numbers of citations, normalized total citations, data, and scopes of the research.

Deng [1] investigated grey systems and their potential using control problems. Initially, the grey system was explained as a concept that contained knowns and unknowns. The concept of a grey matrix was described as a matrix with a part of its properties known and another part unknown. In order to control a grey system, two maps are needed: one from the grey state space to the white state space and the second one from the white state space to the white control space. The author solved a closed-loop polynomial in two steps. The first one is converted from a closed-loop characteristic polynomial into a normal polynomial problem while, in the second step, the result can be obtained. Deng J. L. from China is the only author that performed the research, achieving a total of 3251 citations, with almost 3000 more citations than the author in second place, which shows how relevant the information was for grey systems, representing the first paper published in this area. The average total number of citations was 75.60 with a normalized total citation rate of 2.99.

Bai and Sarkis [46] explored the supply chain domain and the ability of the supplier selection method to adapt to sustainability complexity in order to make the decision process more effective. The scope of the analysis was to present the grey system method and the insights of the technique in sensitivity analysis since the actual papers were limited due to numerous reasons. The use of the grey system is an effective and realistic method used in supplier selection and the results have provided managerial insights, offering ideas for future research. There are two authors, from China and the USA, who achieved a total of 592 citations, with an average total number of citations per year of 39.47 and a normalized total citation rate of 46.35.

Kayacan et al. [47] investigated the Grey Verhulst model, a modified grey model used in the Fourier series, which was developed for time series forecasting. Due to the lack of methods that were unable to forecast with high accuracy, in a smooth manner, the time series, the Grey Verhulst model was tested on USD–EUR parity data between 1 January 2005 and 30 December 2007, comparing results with fuzzy predictors, evolutionary and genetic algorithms, and artificial neural networks. The results showed greater accuracy for grey models for model fitting and forecasting, with the Fourier series being the best algorithm. There are three authors, from Turkey and Canada, that contributed to the research, having a total citation rate of 582, an average total number of citations per year of 38.80, and a normalized total citation rate of 45.56.

Wu et al. [48] presented why the perturbation theory of the least-squares algorithm was used in order to discover the traditional accumulated generating operators that infringe grey systems theory. Using a new model that was created, combining the grey systems method and fractional order accumulation, the authors aimed to identify when the accumulation order number became smaller in the in-sample algorithm, and the results offered a perspective on the performance of the grey model, which was much higher compared with that of the traditional grey model. In total, five authors from China worked in the creation of the article, obtaining a total of 499 citations, with an average total number of citations per year of 41.58 and a normalized total citation rate of 45.56.

Raj et al. [49] analysed the implementation of Industry 4.0 in the manufacturing domain and the academic literature, identifying 15 barriers, which were evaluated using the Grey Decision-Making Trial and Evaluation Laboratory (DEMATEL) model. The most significant barrier was represented by the lack of an existing digital strategy and resources. The results provided an overview of the Industry 4.0 implementation, which would have been much smoother if the standards and government regulations had facilitated the implementation of new technologies. The research presented, also, the challenges in the diffusion of technological innovations, highlighting the benefits of the implementation of Industry 4.0, which could facilitate the work of decision makers. There were five authors that contributed to the research, from India and France, achieving a total of 461 citations, with an average total citation rate per year of 92.20 and a normalized total citation rate of 26.32.

A summary of the mentioned papers is provided in

Table 7. Top 5 most cited documents.

No.	Paper (First Author, Year, Journal, Reference)	Number of Authors	Region/Country	Total Citations (TC)	Total Citations per Year (TCY)	Normalized TC (NTC)
1	Deng JL., 1982, Systems & Control Letters, [1]	1	China	3251	75.60	2.99
2	Bai C., 2010, International Journal of Production Economics, [46]	2	China, USA	592	39.47	46.35
3	Kayacan E., 2010, Expert system theory-based models in time series prediction, [47]	3	Turkey, Canada	582	38.80	45.56
4	Wu LF., 2013, Communications in Nonlinear Science and Numerical Simulation, [48]	5	China	499	41.58	48.16
5	Raj A., 2020, International Journal of Production Economics [49]	5	India, France	461	92.20	26.32

.

Table 8. Brief summary of the content of top 5 most global cited documents.

No.	Paper (First Author, Year, Journal, Reference)	Title	Data	Purpose
1	Deng JL., 1982, Systems & Control Letters, [1]	Control problems of grey systems	No data were used	To investigate the stability of a grey system that has a triangular state matrix
2	Bai C., 2010, International Journal of Production Economics, [46]	Integrating sustainability into supplier selection with grey system and rough set methodologies	No data were used	To explain the grey systems approach in supply chain domain and in supplier selection method, having benefits for sustainability of the processes
3	Kayacan E., 2010, Expert system theory-based models in time series prediction, [47]	Grey system theory-based models in time series production	USD–EUR data parity between 1 January 2005 and 30 December 2007	To describe the possibility of using grey system models in forecasting time series. A comparison between multiple algorithms was performed
4	Wu LF., 2013, Communications in Nonlinear Science and Numerical Simulation, [48]	Grey system model with the fractional order accumulation	No data were used	To detail the combination of grey system and fractional order accumulation that offered higher performance in multiple examples
5	Raj A., 2020, International Journal of Production Economics [49]	Barriers to the adoption of Industry 4.0 technologies in the manufacturing sector: An inter-country comparative perspective	No data were used	To present the importance of Industry 4.0 technologies and how the process of implementation is delayed due to a number of barriers, which were analysed using Grey Decision-Making Trial and Evaluation Laboratory (DEMATEL) model

presents the most global cited documents together with the first authors, years of publication, journals, titles, data, and scopes of the analyses.

3.6. Mixed Analysis

In this section, the focus will be on thematics that are included in grey systems theory papers, together with the factorial analyses, WordClouds, collaboration networks of the authors, and which are the most used bigrams and trigrams in titles and abstracts.

Figure 13 describes the most influential Keywords Plus, grouped in three clusters based on the thematics. On the top right part of the graph, in Motor Themes, is the highest cluster, which has high density and centrality values. The cluster focuses on grey system applicability areas and statistical methods: “prediction” (473 appearances), “China” (238 appearances), “algorithm” (212 appearances), “consumption” (206 appearances), “demand” (189 appearances), “energy-consumption” (187 appearances), “forecasting-model” (146 appearances), “electricity consumption” (140 appearances), “prediction model” (130 appearances), and “co2 emissions” (115 appearances). The presence of China in the cluster outlies how crucial Chinese authors have been to the evolution of the grey systems domain. The second cluster, coloured green, is in the middle of all four quadrants, having medium density and centrality values. The cluster express the main steps that must be applied in order to use grey systems: “model” (717 occurrences), “performance” (247 occurrences), “management” (223 occurrences), “selection” (187 occurrences), “systems” (171 occurrences), “design” (157 occurrences), “framework” (97 occurrences), “relational analysis” (89 occurrences), “quality” (84 occurrences), and “decision-making” (81 occurrences). In the bottom left part of the graph is the smallest cluster, the red one, which has reduced values for density and centrality. The most representative terms included in cluster are “optimization” (314 appearances), “system” (304 appearances), “impact” (108 appearances), “efficiency” (71 appearances), “grey” (71 appearances), “network” (70 appearances), “energy” (69 appearances), “time” (56 appearances), “behavior” (53 appearances), and “simulation” (50 appearances). Similar results were observed in the paper published by Prakash et al. [30], with “model”, “optimization”, “performance”, “prediction”, “algorithms”, and “management” as the main keywords utilized in grey systems.

Figure 14 includes the thematic map of authors’ keywords, grouped in two clusters.

The blue cluster, which is in the bottom right part of the graph, in the Basic Themes quadrant, shows a small value for density and a high centrality value. The terms that are part of the blue cluster are related to the grey systems area: “grey model” (614 appearances), “grey system” (374 appearances), “grey prediction” (353 appearances), “prediction” (269 appearances), “forecasting” (268 appearances), “grey prediction model” (211 appearances), “genetic algorithm” (117 appearances), “gm(1,1) model” (117 appearances), and “neural network” (113 appearances). In the opposite part of the graph is pointed out the second cluster, with the red colour and which is much smaller, which is focusing on grey methods and applications such as “grey theory” (603 occurrences), “grey system theory” (516 occurrences), “grey relational analysis” (220 occurrences), “grey clustering” (133 occurrences), “grey incidence analysis” (127 occurrences), “grey system theory” (103 occurrences), “grey systems” (99 occurrences), “uncertainty” (99 occurrences), and “grey number” (94 occurrences). Prakash et al. [30] had similar results while investigating grey systems, finding ”model” or “grey algorithms”, while Pan et al. [28] considers, as the most relevant keywords in grey systems theory, “grey model” and “forecasting accuracy”.

Figure 15 explores the 100 most used Keywords Plus, grouped in three clusters. The most significant cluster is coloured in red and focuses on applicability domains such as “electricity consumption”, “natural gas”, “energy consumption”, and “climate change” by using grey system methods such as “swarm particle optimization”, “classification”, or “regression” in order to minimize the “risk”. Also, “China” is part of the red cluster, showing the importance of the country in the evolution of the grey systems area. The blue cluster, which contains fewer terms, focuses on the supply chain domain, one of the areas where grey system applications have offered great results. The most representative terms are “supply chain”, “management”, “supplier selection”, and “ahp” and “dematel” methods, which facilitate the decision-making processes by taking into consideration multiple criteria and supporting business goals. The last cluster, the green one, refers to “carbon emissions”, which could affect “countries” and their “economic growth”. A factorial map has been implemented also by Delcea et al. [27], pointing out “energy consumption”, “sustainable development”, “electricity consumption”, “economic growth”, and “economic development” as the main keywords.

Figure 16 details the factorial analysis of 100 title terms, which have been grouped in three different clusters. In Figure 16, the red cluster, which is the most representative, includes various terms related to grey systems, such as “networks”, “evaluation”, “relational”, or application domains “supply”, “control”, “estimation”, “research”, “risk”, and “industry”, or methods including “fuzzy”, “fault”, “gm”. The second cluster, coloured in blue, is smaller compared to the red one, but it is also crucial, containing information about the most productive country in theacademic domain, China, and various grey system methods such as “nonlinear”, “optimized”, and “discrete” and noting where the methods have the highest accuracy: “electricity”, “consumption”, “carbon”, “emissions”, “gas”, and “demand”. The green cluster, which is the smallest, expresses information about “neural network” and “short term memory” methods.

Figure 17 includes the thematic evolution for Keywords Plus in three different time periods, between 1982 and 2000, 2001–2015, and 2016–2024. For the first period, the most used keywords are “algorithm”, “optimization”, “system”, “energy transfer”, “uncertainty”, and “models”. Between 2001 and 2015, “algorithm”, “optimization”, “system”, and “energy transfer” were replaced by “model” while “uncertainty” was replaced with “performance” and “models” remained unchanged. In the last period, between 2016 and 2024, “model” was divided into two parts: it was kept as “model” but also used “prediction”. The “performance” keyword was replaced with “model” while “models” was replaced with “risk”. The thematic evolution has been defined also by other authors of the academic community, illustrating the evolution of the domain, which began with generic terms and evolved into specific and technical keywords [27].

Figure 18 is correlated with Figure 17, representing the thematic map of the Keywords Plus included in thematic evolution. There are three clusters, with different terms included and different sizes, divided based on their importance. The most significant cluster is presented at the border of the Basic Themes quadrant and Motor Themes, with a high centrality and a medium density. The most used terms that are part of the cluster are “prediction” (334 occurrences), “optimization” (241 occurrences), “China” (216 occurrences), “system” (203 occurrences), “consumption” (192 occurrences), “algorithm” (155 occurrences), “demand” (150 occurrences), “electricity consumption” (138 occurrences), and “forecasting-model” (120 occurrences). The second cluster, coloured green, is at the border between Emerging or Declining Themes and Basic Themes, with a very small value for density and a medium value for centrality. The most representative Keywords Plus are “model” (558 appearances), “management” (223 appearances), “performance” (202 appearances), “selection” (145 appearances), “impact” (136 appearances), “design” (109 appearances), “framework” (88 appearances), “systems” (88 appearances), “quality” (72 appearances), and “decision-making” (59 appearances). The last cluster, which is on the top left part of the graph, has a small value for centrality and a high value for density. The most relevant terms are “risk” (135 occurrences), “survival” (95 occurrences), “mortality” (89 occurrences), “outcomes” (69 occurrences), “disease” (58 occurrences), “diagnosis” (51 occurrences), “health” (44 occurrences), “association” (43 occurrences), “prevalence” (37 occurrences), and “epidemiology” (33 occurrences). According to the a segment of the academic community that has been studying the grey systems field, the most representative terms for thematic evolution are “model”, “performance”, “management”, “optimization”, and “prediction”, which confirms the outcome discovered during bibliometric analysis [30].

Figure 19 explores the collaboration network involving the 50 most influential authors. There are nine clusters presented, which will be detailed separately. The first cluster, coloured in green, contains nine authors: Liu S. F., Xie N. M., Yang Y. J., Fang Z. G., Wu LF., Chen Y., Zhang K., Mi CM., and Wang H. Liu S. F. is pointed out among the rest of the authors, which represents the importance of the author in the domain, having numerous articles published on the commercial aircraft domain by forecasting the costs or analysing the measures of information for grey numbers or predicting the lifetime of mica paper capacitors. Liu S. F. also analysed the supply chain management domain by using multiple attributes for decision-making on the mean values of grey numbers or to predict energy consumption using grey models [50,51,52,53,54]. Xie N. M. focused on uncertainty information and the representation measurement of grey numbers, the construction of whitenisation mechanism functions, and the applicability using the grey clustering method; a grey incidence cluster model was used to identify the complex equipment’s development cost [55,56,57]. Mi C. M.’s research was on using grey nonlinear clusters in order to investigate the credibility level of trustworthy software, analysing the supply chain domain by using multiple attributes for decision-making for the mean values of grey numbers and clustering the whitenisation weight function using grey methods [54,58,59].

The second cluster, coloured in blue, is formed by only two authors: Xiao X. P. and Duan H. M. The focus of the authors was on short-term traffic and traffic flow mechanisms using grey systems [60,61,62].

The third cluster, coloured in red, contains 25 authors: Wang Y., Zeng B., Liu Y., Zhang Y., Wang L., Zhang L., Wang J., Liu J., Ma X., Li Q., Zhang J., Li J., Li L., Li H., Luo YX., Chen L., Wang X., Wang C., Luo D., Yang Y., Wang Z. Y., Wang Q., Li C., Wang J. Z., and Wang W. The majority of the authors are from China, and the focus was on the optimum allocation of water while taking into account the uncertainties, biogas forecast, main power grid prediction and policies in China, hazard assessment using grey systems, irrigation control technology, energy production in China, and many other applications [63,64,65,66,67,68].

The fourth cluster, coloured in pink, contains eight authors, Dang Y. G., Li Y., Wang ZX., Wang Y. H., Li XM., Liu B., Ding S., and Wang J. J, focusing on virtual machine consolidation strategy together with energy-awareness for cloud computing platforms by using grey models, building and solving the whitenisation weight function by using grey numbers, and calculating the degree of greyness for grey numbers [69,70,71].

The last five clusters, numbers 5 (coloured in orange), 6 (coloured in brown), 7 (coloured in pink), 8 (coloured in grey), and 9 (coloured in turquoise), contain only 1 author each: the orange cluster is formed by Liu C., the brown cluster contains Hu Y. C., the pink cluster contains Nagai M., the grey cluster is formed by Xie W. L., and the last cluster contains Li G. D. The authors explore the possibility of predicting the energy consumption or forecasting using the interval grey method for energy demand, predicting machining accuracy, forecasting the retail sales of consumer goods by using the discrete grey polynomial model, or identifying the solution of the supplier selection problem using grey methods [65,72,73,74,75].

Table 9. Top 10 most used bigrams.

Bigrams Titles	Frequency Bigrams Titles	Bigrams Abstracts	Frequency Bigrams Abstracts
Grey model	744	Grey model	2711
Prediction model	401	Prediction model	1976
System theory	346	System theory	1552
Model based	322	Neural network	1307
Neural network	285	Proposed model	953
Relational analysis	160	Prediction accuracy	885
Energy consumption	141	Time series	832
Time series	107	Energy consumption	797
Supply chain	96	Forecasting model	693
Evaluation model	88	Experimental results	546

contains the bigrams that are pertinent to investigating the grey systems domain, removing those that are synonyms and related to search terms. The first two columns focus on title bigrams while the last two are on abstracts. The first and third bigrams are describing the key parts of grey systems, “grey model” with 744 appearances and “system theory” with 346 occurrences. The terms “prediction model” (401 appearances), “model based” (322 appearances), “neural network” (285 appearances), “relational analysis” (160 appearances), “time series” (107 appearances), and “evaluation model” (88 appearances) focus on the statistical and mathematical approach of the domain. Two of the main applications of grey systems are also detailed: “energy consumption” (141 appearances) and “supply chain” (96 appearances). On the right part of the table are presented the 10 most used bigrams in abstracts, which can be divided into three categories: the first one includes grey system information with terms such as “grey model” (2711 occurrences) or “system theory” (1552 occurrences), the second category encapsulates the statistical methods with terms such as “prediction model” (1976 occurrences), “neural network” (1307 occurrences), “proposed model” (953 occurrences), “prediction accuracy” (885 occurrences), “time series” (832 occurrences), “forecasting model” (693 occurrences), and “experimental results” (546 occurrences), and the last cluster includes the “energy consumption” area, where grey systems have been successfully applied. Delcea et al. [27] evaluated grey systems theory, extracting the most representative bigrams for titles and abstracts as the following: “grey model” (357 appearances), “energy consumption” (328 appearances), “supply chain” (231 appearances), and “prediction model” (229 appearances). They showed an overlap between the identified bigrams for grey systems theory.

Table 10. Top 10 most used trigrams.

Trigrams Titles	Frequency Trigrams Titles	Trigrams Abstracts	Frequency Trigrams Abstracts
Grey systems theory	300	Grey systems theory	1304
Grey prediction model	213	Grey prediction model	810
Prediction model based	55	Bp neural network	273
Neural network model	41	Particle swarm optimisation	263
Particle swarm optimisation	38	Evaluation index system	181
Support vector machine	31	Artificial neural network	161
Power load forecasting	29	Prediction model based	136
Natural gas consumption	24	Natural gas consumption	117
Artificial neural network	23	Hierarchy process ahp	113
Carbon dioxide emissions	22	Relational analysis gra	109

presents the most used trigrams. In the first two columns, the titles are described, and in the last two, the abstracts are detailed. The most relevant trigrams are “grey system theory” (300 occurrences), “grey prediction model” (213 occurrences), “prediction model based” (55 occurrences),“neural network model” (41 occurrences),“particle swarm optimization” (38 occurrences),“support vector machine” (31 occurrences),“power load forecasting” (29 occurrences),“natural gas consumption” (24 occurrences),“artificial neural network” (23 occurrences), and “carbon dioxide emissions” (22 occurrences). On the right side of the table are detailed the most used trigrams in abstracts. In first place is “grey system theory”, which appeared 1304 times, followed by ”grey prediction model” with 810 occurrences. In third place is “bp neural network” with 273 appearances while “particle swarm optimization” and “evaluation index system” appeared 263 and 181 times. The rest of the trigrams have smaller numbers of appearances but are worthy of mentioning: “artificial neural network” (161 appearances), “prediction model based” (136 appearances), “natural gas consumption” (117 appearances), “hierarchy process ahp” (113 appearances), and “relational analysis gra” (109 appearances). In both titles and abstracts, the focus was especially on grey theory, expressing the main characteristic of the area and how to use it, presenting also algorithms and real examples where the models offered great results. According to Delcea et al. [27], the most representative trigrams for titles and abstracts in the case of grey systems used in economic studies are “grey system theory” (131 appearances), “grey prediction model” (113 appearances), “particle swarm optimization” (38 appearances), “hierarchy process ahp” (113 appearances), and “relational analysis gra” (18 appearances), highlighting, once more, the overlapping of the identified trigrams in titles and abstracts, underscoring the unicity of the keywords associated with the studies from various disciplines in the case of grey systems theory.

Figure 20 explores the top 50 most used authors’ keywords and Keywords Plus. Using the Biblioshiny library, which is part of the R programming language, WordClouds have been created, providing graphical representations of the most frequently used terms. The size of the text reflects the number of appearances. On the left part are presented the 50 most used authors’ keywords. The most used term is “grey model” with 616 appearances, followed by “grey theory” and “grey system theory”, with 603 and 516 occurrences. In fourth place is “grey system” with 374 occurrences, and “grey prediction” is fifth with 353 occurrences. The rest of the terms have fewer than 300 appearances but are worthy of mentioning: “prediction” (269 occurrences), “forecasting” (268 occurrences), “grey relational analysis” (220 occurrences), “grey prediction model” (211 occurrences), and “grey clustering” (133 occurrences). The most 50 used keywords on the right part are presented. In first place is “model” with 717 occurrences, followed by “prediction” with 473 appearances and “optimization” with a frequency of 314. In fourth place is “system” with 304 occurrences, followed by “performance” with 247 appearances and “China” with 238 occurrences. In seventh and eighth place are “management” with 223 appearances and “algorithm” with 212 occurrences. The last two terms are “consumption” with a frequency of 206 and “demand” with a frequency of 189. Delcea et al. [27] have discovered similar authors’ keywords and Keywords Plus as the most representative: “model”, “grey theory”, “grey system theory”, “grey prediction”, “forecasting”, and “performance”. Prakash et al. [30] defined a WordCloud for the most utilized keywords between 2011 and 2021 as having “grey systems”, “grey systems theory”, “decision making”, “forecasting”, or “grey incidence analysis”. Some of the keywords were common with the outcome that was extracted from our dataset, but at the same time, there were different keywords that have higher frequencies, with all of them being related to grey systems theory.

Lastly, an analysis regarding the connections between authors, their organisations, and the keywords used in the extracted dataset is depicted in Figure 21. As can be observed, the authors included in the analysis are sometimes connected to more than one university while the keywords used are related, as expected, with various aspects from grey systems theory, such as grey systems in general, the grey model, grey incidence analysis, grey clustering, grey forecasting, and the grey GM(1,1) model.

4. Discussion and Limitations

The focus of this section is to describe the main limitations that have been observed during the research, together with the outcome of the scientific analysis.

4.1. Main Bibliometric Results and Comparison with Similar Studies

The bibliometric approach included a comprehensive analysis of grey systems theory, starting with 1982, when the domain was founded by the Chinese Professor Deng Ju-Long, which represented the baseline for all the other documents. Thanks to technological evolution, the area has evolved in a significant manner, having had 649 papers published in 2022, 563 documents in 2023, and 420 papers in 2024.

The grey systems theory domain has become one of the most interesting topics for Chinese researchers. China is the leading country, with 7487 papers published and 74,567 citations. In second place, with a very big difference, is India, with 240 articles published; these have 4686 citations. In third place is the USA, with 175 documents and 4862 citations, followed by Iran and Turkey, with 123 and 107 papers, with 1699 and 3626 citations. The Chinese influence is observed also in the most significant universities, having six affiliations in the top 10, the Nanjing University of Aeronautics and Astronautics, Chinese Academy of Sciences, North China Electric Power University, Wuhan University of Technology, Hebei University of Engineering, and Nanjing University of Information Science and Technology. Delcea [76] explored the grey systems theory articles that had been released using a bibliometric approach and the country with the most number of publications was China. Pan et al. [28] explored the countries with the most numbers of publications and found China, the USA, India, Japan, Iran, Turkey, the UK, and Canada as some of the most relevant.

Various journals have started to publish documents related to grey systems theory in the last years. The most relevant ones are Journal of Grey System; Grey Systems: Theory and Application; Expert Systems with Applications; Proceedings of 2007 IEEE International Conference on Grey Systems and Intelligent Services, Vols 1 and 2; Mathematical Problems in Engineering; Sustainability; Energy; Kybernetes; Journal of Cleaner Production; and Applied Mathematical Modelling. Similar papers were analysed, and the results discovered were comparable. Yin [4] analysed 15 years of grey systems theory by using a bibliometric approach and found, as some of the most influential journals, Journal of Grey System, Expert Systems with Applications; and Energy. Pan et al. [28] found the most journals on grey systems theory: Journal of Grey System, Proceedings of 2007 IEEE International Conference on Grey Systems and Intelligent Services, Kybernetes, Energy, Grey Systems: Theory and Application, Expert Systems with Applications; and Mathematical Problems in Engineering.

4.2. Discussions on Specific Themes

The scope of the sub-section is to detail the main themes that have been discovered among the datasets that have been analysed, demonstrating the versatility and applicability of grey systems theory.

4.2.1. Applicability of Grey Systems Theory in Sustainability and Sustainable Technologies

Grey systems have a significant impact on sustainability, representing one of the topics with the highest variety of solutions proposed by the grey domain. Taking into consideration the existing papers on the topics, Wang et al. [77] evaluated the alternative solutions to the fossil energy industry by combining grey theory and Data Envelopment Analysis (DEA) in order to identify the inefficient units for sustainable development in the Vietnamese coal industry. One of the main key indicators was the location of coal mines, suggesting various collaborations among mines, such as between the Cao Son and Coc Sau coal mines and between the Nui Beo and Vang Danh coal mines. The coalition between coal mines could lead to more effective processes, sharing risks and resources and increasing cooperation, since the distances between mines were relatively small. The model that was estimated used data from 2017 to 2021, having a highly accurate outcome compared to similar papers.

The cryptocurrency sector represents a new economic segment that has become more and more popular in the last years, and some of the works in this field have considered the advantages offered by grey systems theory when dealing with uncertainty situations. For example, Yin et al. [78] created a novel multiple-attribute group decision-making (MAGDM) model that calculates the sustainable development of the main cryptocurrencies based on the similarities. Using Pythagorean fuzzy numbers, the membership function, and the whitenisation weight function, a rigorous analysis of major decision-making elements was performed, together with the sustainable evaluation of cryptocurrencies that had been included in research within numerical applications that had assigned weights, in order to understand the impact on ranking. The most sustainable cryptocurrency was Stellar while Bitcoin was the cryptocurrency that consumed the most energy since it has a high cost for computing and mining.

Su et al. [5] explored the supply chain management topic from an environmental perspective, implementing a Grey-DEMATEL solution that extracts the main criteria for supplier prioritisation, containing information related to communities for sustainability, sustainable plans, sustainable certification and growth, and other features. The purpose of the analysis was to investigate and evaluate the hierarchical structure in order to obtain the main criteria for supplier selection. Due to the uncertainty and lack of information, grey systems theory has been successfully implemented, obtaining material savings, which stands as the top criterion for supplier selection.

Analysis of the sustainable initiatives in scientific literature has also been conducted through the use of grey systems theory methods, especially the ones dedicated to decision-making in the context of choosing the appropriate policies that should be implemented. Luthra et al. [79] implemented a Grey-DEMATEL method for extracting the most relevant Critical Success Factors (CFSs) for sustainable initiatives in the domain of supply chain management in the Indian context, identifying a total of 15 measures in the existing literature. For a better understanding of the relationship among the extracted CSFs, a Grey-DEMATEL model was used, grouping the factors in two different groups: cause and effect. The Grey-DEMATEL was able not only to manage and solve the uncertainty decisions but also to evaluate the causes and effects of the factors. Continuous supervision is highly recommended for the CSFs in order to be sure that they are implemented correctly.

Due to the complexity and uncertainty, the correctness of the decision taken in various contexts becomes of utter importance. As a result, Ulutaș et al. [80] integrated a Grey Best–Worst Method (BWM), together with a Grey Weighted Sum–Product model, in order to select the optimum supplier for the textile manufacture sector based on three criteria and twelve sub-criteria. Since there was a significant uncertainty in the data and the dataset was relatively small, grey systems theory represented the best solution. The outcome was presented to the experts that confirmed the accuracy of the model. The advantage of multi-criteria decision-making is the possibility of applying the model to any other domain that has multiple criteria and suppliers or alternatives.

Taking into account the research that has been presented above, grey systems theory has numerous applications in the sustainability area, focusing in general on sustainable development measures [5], energy efficiency [77,78], and process optimisation [79,80].

4.2.2. Applicability of Grey Systems Theory in Risk Assessment and Economic Activities in General

The economic sector includes a wide range of applications that have been developed for risk analysis, supply chain management, and many other commercial operations, representing one of the most crucial subjects for grey systems theory.

A digraph matrix and grey systems theory have been implemented by Rajesh et al. [81] in order to diagnose and measure the main supply chain management methods’ adverse effects. A total of 12 primary hazards and 21 risk mitigation measures have been found for the electronics manufacturing industry. To demonstrate the potential of grey systems theory, a case study on an Indian company that produces electronic components has been defined. The outcome has demonstrated the positive correlation between risk mitigation techniques and values, providing several future strategies for supply chain management.

Li et al. [82] extracted the major risk factors, together with the local investment environment risk, organisation management risk, technical risk, safety, management, economic risk, health, or social responsibility risk. Qualitative and quantitative approaches based on grey systems theory and fuzzy mathematics were performed for a risk evaluation, analysing the investment risks for a Chinese oil refining project. The results demonstrated the data on accuracy, validity, and robustness for future investment in the oil refining domain, offering theoretical and practical solutions, taking into consideration the real risks, measures, and solutions.

Thanks to the development of the topic, grey systems have been successfully implemented in the analysis of interstellar gas and multigroup radiation hydrodynamics, calculating the collapse and formation of Larson’s core by Vaytet et al. [83]. Authors have explained star formation as a complex process that starts with gravitational collapse. The focus of the research is on a multitude of simulations that demonstrate the lack of radiative transfer that should have been generated by thermal energy, which is explained by the central density, which might be similar within the grey and multigroup simulations, resulting in a small difference between the solutions. The outcome from the grey model explains the radiative transfer that occurs in specific simulations for protostellar collapse, and at the same time, the multigroup radiative transfer can be used in the long term for protostars.

The unstable evolution of energy market has been pointed out by Li et al. [84] due to the unbalanced evolution of energy consumption, energy prices, and economic growth. The author’s approach consists of a nonlinear grey model that takes into consideration, as a group, energy consumption, economic growth, and energy prices and, thanks to the least-squares method, estimates the parameter formula for the group. The algorithm was also applied for the estimation of coal consumption and prices in China between 2021 and 2025, defining theoretical and practical methods that should be taken for a stable Chinese energy system, representing an initial development of energy and environmental methods that should be implemented, further investigation being necessary.

Urbanisation, energy consumption, and economic growth are considered crucial for energy consumption estimation for the Chinese market, and Wang and Cao [85] explored the domain in order to formulate policies that should be implemented using a multiple-grey-systems mode. Numerous models have been tested, but the highest accuracy has been registered for the multivariate grey prediction model (MGM), with a value of 97%. The estimation has been completed for energy consumption, economic growth, and urbanisation between 2020 and 2025, offering a perspective for the future plans and policies that should be adopted. China has to continue the trends and to be aware of energy consumption levels that could affect urbanisation and economic growth.

According to the information that has been described above, the economic activities and risks are strongly correlated with grey systems theory, providing a comprehensive overview on urbanisation [85], energy consumption [85,86], economic development, or risk analysis [81,82].

4.2.3. Applicability of Grey Systems Theory in Medicine and Biology

Medicine and biology can be considered key fields in human evolution due to the revolutionary development that has been made. Grey systems have been successfully implemented in the medicine field, with numerous applications that will be further presented.

The purpose of the research conducted by Raymundo et al. [87] was to evaluate the existing risks in the medical area, focusing on the paediatric segment. The dataset was obtained from the United Network for Organ Sharing, with information about 5542 patients, aged between 0 and 18, that were on the waitlist, using data between January 2010 and June 2019. The major factors that could be associated with the waitlist mortality of the patients were identified using the Fine–Grey model, being tested on two thirds of the dataset and validated on a third of the patients, with an ROC curve value of 0.762. The main factors that were identified were weight, blood type, the presence of ventilator support, creatine level, and region.

The biomedical sector has successfully implemented grey system methods, as Lv [88] presented. Thanks to the technological evolution of the biomedical sector, competitiveness has increased significantly, developing new products that are of high quality. A case study on the Chinese biomedicine industry has been performed from two perspectives, technological development and technological transformation, using the grey relational clustering model. A panel data with information between 2012 and 2018 was utilized, which confirmed the unbalanced evolution of the industry among the Chinese regions.

One of the most historical and representative traditions for Chinese people is Chinese traditional medicine. Thus, in their paper, Li-Zhong et al. [89] focused on Chinese traditional medicine in order to increase population health, to promote the local culture and social harmony, and to develop economic benefits. Chinese traditional medicine represents a unique treasure for the locals, representing a combination of philosophical ideas and human spirit. Grey Relational Analysis and Grey Clustering Analysis were implemented for establishing the main factors of Chinese traditional medicine. The outcome confirmed that the behavioural mechanisms were strongly correlated with the lack of information and uncertainty. The algorithms provided several recommendations for the Chinese medicine sector.

Zhou [90] presented the equity of health resources in traditional Chinese medicine and how it could be predicted for the 14th Five-Year Plan period using a grey prediction model that calculated the health resources evolution. The results presented the concentration index of traditional Chinese medicine institutions and number of beds. For the regions with less economic development, the index value was negative while for practitioners and pharmacists, the concentration index was positive, especially in the regions with high economic development.

One of the benefits of the development of grey systems theory is the implementation of solutions in multiple areas, and the best example is for medicine, which has been investigated above. The main objectives are to evaluate the risks in the biomedicine sector [87,88,91] and traditional Chinese medicine methods [89,90].

4.2.4. Applicability of Grey Systems: Renewable Energy Sources

Renewable energy sources have developed significantly in the last years due to the necessity of the reduction of greenhouse gas emissions and new green sources that can produce energy and protect the environment.

The CO₂ emissions in China represent one of the main topics wherein grey systems theory has a variety of applications. Dai et al. [92] explained the impact of CO₂ emissions in China, which generates approximately 28% of the global level. The scope of the research was to provide sources to reduce the percentage. The initial step was to accurately predict the emissions and to formulate the main policies and solutions that should be implemented for making reductions in greenhouse gas emissions. The grey model and least-squares support vector machine methods have been developed for estimating CO₂ levels. The main factors that could impact CO₂ emissions are the GDP per capita, industrial structure, energy consumption, energy intensity, level of urbanisation, population, coal consumption, level of exports and imports, and carbon emission intensity. The grey model analysed the factors and estimated the impact of each feature, calculating also the CO₂ emissions for China between 2018 and 2025.

Thanks to technological development, the battery energy storage sector has improved significantly in the last years. In this context, Khalid and Savkin [93] investigated the battery energy storage system by using a grey systems theory method for simulating operations according to the existing restrictions such as battery power, charging, the discharging rate, the battery capacity, or the state of charge. The model was successfully tested on real data and the results were very effective. The grey model has adaptability and potential to improve the performance of predictive controllers, representing a great start for the implementation of grey systems in the automotive industry and battery energy management.

Yang et al. [94] described the environmental threats that exist and how the rapid economic growth of China affects traditional energy consumption, focusing more on sustainable sources such as wind energy. The distribution, installation, power generation, capacity, and economic and environmental benefits of wind energy systems have been explained. The grey system model has been implemented for forecasting the wind capacity between 2017 and 2025. The outcome of the aforementioned study indicates that the northern region produces the highest amount of wind energy, approximately 2500–3000 giga watts. Inner Mongolia is a region in the north of China that produces a significant amount of wind energy, around 1300 giga watts. China has a strong foundation for the development of wind power systems thanks to the potential and existing wind resources, assuring the sustainable development of renewable energy sources.

As carbon neutrality is a key topic nowadays, Qiao et al. [95] present why it is necessary to build new power systems, together with new energy solutions. One of the best sources is wind power, which produces non-polluting energy. The focus in the paper was to estimate and identify the main investment risks that could appear in wind power projects. A trigonometric function of fuzzy–grey clustering was implemented, which studied the risks of wind power investments in China. According to the results, there is no imminent or huge risk that could block the implementation of wind power technology, and the outcome can be used as a benchmark for investment decisions.

Chaotic theory, the empirical decomposition mode, and grey systems theory were combined for a wind farm power prediction by An et al. [96]. The process began with the decomposition of the wind power farm, resulting in two components, known as the intrinsic mode function and residual. The scope of the grey model was to estimate the residual component, offering great accuracy, and this could be used for a short-term estimation for wind power farms. The prediction with highest accuracy aggregated all intrinsic functions based on their specific characteristics.

The renewable energy sources domain has significant potential thanks to recent investments and the focus of governments on this segment. According to the papers that were analysed, reductions in emissions [92,96], the implementation of wind power farms [94,95], and the battery storage sector [93] represents the main topics.

4.2.5. Applicability of Grey Systems Theory in Real Use Cases

Grey systems theory has evolved from a theoretical field to a practical one, with a variety of solutions for real problems. Rao and Liu [97] described the applicability of grey systems theory in the aviation domain, using physics aspects in order to develop a viable methodology that increased the accuracy of airplane taxiing, based on several uncertain parameters. Thanks to grey systems theory, Wenbin et al. [98] developed a process for thermal environments, which was able to integrate the uncertainties of weather, intervals of cooling loads, solar radiation, thermal disturbances, and outdoor air temperatures. The range of energy consumption could be predicted, based on a specific level of reliability, which was positively correlated (the higher the reliability level was, the more the energy cost would increase). The model is useful not only for consumers, but also for companies, in order to estimate energy consumption and costs in the future. Using Grey Relational Analysis, Wang et al. [85] estimated the annual urban heat supply by taking into account the historical data of heat supply systems, focusing on three cities from China, with a total of 16 factors being extracted. The accuracy of the models provides significant advantages for optimisation consumption, offering an overview of the future annual consumption, providing assistance in organizing and structuring the future energy policies that should be implemented.

From the environmental perspective, grey systems theory demonstrates efficiency, analysing the social impact of hydrocarbon exploration, as Delgado and Romero [99] investigated, focusing on a project from Valencia, Spain, including three stakeholders’ groups and four selection criteria. The outcome demonstrated the negative correlation between social impact and hydrocarbon exploration, representing solid research that should be taken into consideration by the local and central authorities. At the same time, the analysis demonstrated the social impact of multiple energy projects.

As has been presented above, grey systems theory has been implemented successfully in a variety of projects and solutions, optimizing and predicting activities.

4.3. Limitations

Our research led to various limitations, most of them related to the first step of dataset extraction. The first limitation was the fact that only a single database was included in the analysis, ISI Web of Science. Even if the database is one of the biggest and most recognized in the academic community, having various journals and areas indexed, excluding other relevant databases and publications on the same theme could have made the database more diverse, providing different datasets and results. The decision to use ISI Web of Science was further based on the fact that the database offers Keywords Plus, which constitute a unique feature that has the potential to enhance bibliometric analysis by broadening the scope of a study. The Keywords Plus feature enables the extraction of the most used keywords from the references of the papers included in the dataset, providing further information regarding the citations and associated themes.

On the other hand, the use of this database comes with a series of limitations and potential biases related to its emphasis on English-language papers and a limited temporal coverage for older publications as highlighted in Section 2 of the paper—and this is highly dependent on the index one is referring to. Given the specificity of the fields in which grey systems theory has been applied, the use of the ISI Web of Science database had a limited influence on the number of papers included as most of the indexes covered the period after the appearance of the theory. Nevertheless, regarding the emphasis on English-language papers, this was not an issue for the analysis conducted in the paper as, in the extraction steps of the dataset, the condition that all the papers should be written in English was imposed.

Another reason for using the ISI Web of Science database resides in the fact that the dataset extracted from this database is compatible with the software options for the bibliometric analysis, such as Biblioshiny and VOSViewer. It shall be mentioned that both Biblioshiny and VOSViewer are able to process information from specific databases [100]—for example, Biblishiny is supporting data from Scopus, WoS, the Lens Cochrane Library, and Dimensions files [101] while VOSViewer accepts Scopus, WoS, Lens, PubMed, or Dimensions file formats [102], thus limiting the number of databases that can be used for this type of analysis.

Nevertheless, even the option to include information from various databases comes with a series of drawbacks, mostly related to the citation counts. As observed in

Table 11. Example of various numbers of citations based on selected database.

Paper	Number of Citations in Various Databases
	ISI Web of Science (Database Used in This Study)	Scopus	IEEE	Google Scholar
Deng JL., [1]	3251	4197	-	6253

, when changing the database, the number of reported citations varies also. In this case, for exemplification, the paper of Deng [1] has been chosen as it is the most cited paper in our dataset. As can be observed, some of the databases have not indexed it while, among the databases that have indexed the paper, the variety in the number of citations is large.

Furthermore, as acknowledged in the scientific literature, WoS comes with a series of other limitations related to the absence of the authors in the studies included in the dataset [7,103,104] or the regional bias [105]. Even though we acknowledge these limitations, it shall be stated that in the case of the dataset included in our paper, the absence of the authors was not signalled by Biblioshiny in the initial step in which the dataset was scanned.

Table 12. Result of dataset scan before conducting the bibliometric analysis.

Description	Number of Missing Values	Percentage of Missing	Status
Author	0	0.00	Excellent
Document Type	0	0.00	Excellent
Journal	0	0.00	Excellent
Language	0	0.00	Excellent
Publication Year	0	0.00	Excellent
Title	0	0.00	Excellent
Total Citation	0	0.00	Excellent

provides the result of the scan performed with Biblioshiny prior to the analysis of the extracted dataset. As can be observed, none of the authors of the publications included in the dataset were missing.

The second limitation is related to the terms that were used in order to extract the dataset from the WoS database. Only specific keywords were included. This action had an impact on the total number of documents included in the dataset since there, we might have ignored other terms that were referring to the same topic discussed during the research.

The third limitation was the language of the documents that were kept, removing any other papers that had been published in other languages except English. Even if English is an international recognized language, there are papers that have performed comprehensive analysis in other languages and are worthy of being analysed. Since the focus of the research was to evaluate the grey systems theory domain, the inclusion of other papers was not possible as only terms related to the investigated field were used. It should be acknowledged that the exclusion of papers not published in English was a limitation, but it shall be stated that this was determined on purpose, in accordance with the used methodology, in order to assure the relevance of the thematic graphs. The accuracy of the n-gram extraction process and the graphical representation of the thematic map would have decreased significantly if papers in various languages had been included in the analysis. At the same time, the authors have limited proficiency in languages apart from English, which might also be the case for the vast majority of the researchers who will read this paper. Nevertheless, we acknowledge the importance of non-English papers in various areas, as further stated in the scientometric papers from the field [106,107].

5. Conclusions

The paper offers an analysis of the grey systems theory area, starting with 1982, when the first paper was published, up to 2024. Thanks to technological evolution, grey systems theory has also evolved, having had a significant impact in various domains such as energy consumption, biogas, supply chain management, and electricity consumption. Using bibliometric methods, the research that was accomplished was able to extract the main journals, documents, topics, collaboration network, main authors, keywords, thematic maps, and thematic evolution. In order to present the results obtained, the responses to the scientific questions that were described in the first section are elaborated in the following part:

• The main topics discussed in grey systems theory are divided into multiple parts: the main focus is on “Grey systems theory” and “Grey prediction models”, which have become more and more popular for various domains. On the other hand, we have methods such as “support vector machine”, “particle swarm optimization”, “neural network model”, “time series models”, and “artificial neural network” and the main areas where the algorithms can be implemented: “power load”, “natural gas”, “supply chain management”, “energy consumption” or “electricity consumption”, “traffic flow mechanism”, “short-term traffic”, or “decision-making”.
• The most representative affiliations that have contributed to the evolution of the grey systems theory domain are the Nanjing University of Aeronautics and Astronautics (821 documents), the Chinese Academy of Sciences (238 documents), the North China Electric Power University (220 documents), the Wuhan University of Technology (216 documents), Assistance Publique Hopitaux Paris (185 documents), Universite Paris Cite (150 documents), the Hebei University of Engineering (149 documents), the University of California System (142 documents), the University of Toronto (139 documents), and the Nanjing University of Information Science and Technology (137 documents). There are six universities in the top ten from China, two from France, one from the USA, and one from Canada, which points out the implications of Chinese researchers in the analysed domain.
• The collaboration between authors has been divided into nine clusters. The most influential one is the first cluster, where are presented some of the most relevant authors for grey systems theory, such as Liu S. F., Xie N. M., Yang Y. J., Fang Z. G., Wu LF., Chen Y., Zhang K., Mi C. M., and Wang H. The authors have focused on supply chain management, whitenisation, credibility level of trustworthiness, decision-making, or predicting the equipment’s development cost.
• The most relevant authors, based on the number of publications, that have contributed to the development of grey systems theory have been highlighted, with Liu S. F. (354 papers) emerging as a key figure in the area.
• The main journals that have published articles that focused on grey systems theory are Journal of Grey System (468 articles); Grey Systems: Theory and Application (250 articles); Expert Systems with Applications (123 articles); Proceedings of 2007 IEEE International Conference on Grey Systems and Intelligent Services, Vols 1 and 2 (117 articles); Mathematical Problems in Engineering (107 articles); Sustainability (105 articles); Energy (104 articles); Kybernetes (90 articles); Journal of Cleaner Production (80 articles); and Applied Mathematical Modelling (69 articles).
• The countries that have contributed the most to the evolution of grey systems theory, based on the numbers of publications and citations, are the following: China with 7487 publications and 74,567 citations, India with 240 publications and 4686 citations, the USA with 175 publications and 4862 citations, Iran with 123 publications and 1699 citations, Turkey with 107 publications and 3625 citations, the UK with 84 publications and 2958 citations, Japan with 70 publications and 1490 citations, Poland with 59 publications and 543 citations, Canada with 53 publications and 2342 citations, and Romania with 47 publications and 232 citations.

Regarding the main findings that has been discovered in the area of grey systems, it shall be mentioned that numerous applications are available, especially in the sustainability, business, and medicine areas, supported by the scientific researchers that have investigated these topics. Thanks to the development of the domain, grey systems can be combined with Artificial Intelligence, Machine Learning, risk analysis, and many other methods that can promote a sustainable development for the environment [5,77,79], economic activities [81,82,83], medicine or biology [87,88,89], and renewable energy [93,95,96].

The outcome of the research presents the main domains and approaches for grey system implementation in various industries according to the dataset that has been analysed. Regarding sustainable development, the main solutions that have been implemented are Data Envelopment Analysis, the whitenisation function, the DEMATEL method, and the Best–Worst Method, all combined with grey systems theory, in order to optimize coal mine activity and collaboration, to evaluate the energy consumption of cryptocurrencies, or to identify the optimum supplier for the manufacturing industry [77,78,80]. On the economic side, there are numerous applications, especially in risk analysis, energy consumption, energy prices, economic growth, and energy policies. Grey systems have been implemented combined with fuzzy mathematics methods, the least-squares method, and least mean square or neural network methods [82]. In medicine and biology, the most used methods are grey relational clustering, Grey Relational Analysis, and Grey Clustering Analysis, used for evaluating the risks, to increase the Chinese population’s health, to promote social harmony and local culture, and to bring economic benefits [87,88,89]. The main focus on renewable energy aims to reduce greenhouse gas emissions, to implement wind power sources, or to optimize battery energy storage systems by implementing grey systems and the fuzzy–grey clustering method [92,93,94,95,96].

Future research in the field of grey systems theory might take these data into consideration to continue the progress that has been achieved, especially in sustainability, supply chain management, supplier selection, heating systems, aviation, and medicine, starting from Rao and Liu [97], Lv [88], Dai et al. [92], or Rajesh et al. [81] by developing more complex and relevant applications for stakeholders, communities, and governments. At the same time, evaluating the impact of grey systems theory in various domains could bring more information and insights related to authors, countries, journals, and universities in domain-specific fields.