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The purpose of this paper is to review systematically the research of grey relation analysis (GRA) models.

Three different approaches, the springboard to build a GRA model, the angle of view in modelling, and the dimension of objects, are analysed, respectively.

The GRA models developed from the models based on relation coefficients of each point in the sequences in early days to the generalized GRA models based on integral or overall perspective. It evolved from the GRA models which measure similarity based on nearness, into the models which consider similarity and nearness, respectively. The objects of the research advanced from the analysis of relationship among curves to that among curved surfaces, and further to the analysis of relationship in three‐dimensional space and even the relationship among super surfaces in n‐dimensional space.

The further research on GRA models is proposed. One is about the property of GRA model. An in‐depth knowledge about the properties of GRA model will help people to understand its function, applicable area and requirements for modelling. The other one is about the extension of research object system. The object to be analysed should be extended from the common sequence of real numbers to grey numbers, vectors, matrices, and even multi‐dimensional matrices, etc.

As the grey systems theory has been widely used in the field of sustainable development (SD) research, in the following, a short literature overview will be put forward, starting from the usage of these theories in the economic development, social inclusion and environmental protection contributions to the evolving process of SD during 2011–2021. The purpose of this paper is to identify some key studies from all the SD areas in which the grey systems can be used in order to open and to bring the researchers to new domains in which they can reveal their interest and in which they can successfully use the methods offered by the grey systems theory.

Using the search engine offered by the Google Scholar and the Web of Science (WoS), a literature review has been performed for the grey systems applications on SD research on both grey relational analysis (GRA) and grey forecasting. In addition, some grey evaluation theories – clustering evaluation models and grey target decision models – have also been presented.

Many grey models are widely used in the field of SD. Compared with other methods such as grey prediction, grey evaluation and decision-making model, GRA technology is the most used method, and the research using this method is more than three times that of all other methods.

The present paper identifies some of the most representative examples in which the grey system theory (GST) has been used, but, in the same time, there are a lot of studies that have not been mentioned here due to the lack of space.

The present paper focuses on the SD applications in which GST has been successfully used, bringing to the reader a general overview on this field and, in the same time, enables new research perspectives.

This paper aims to apply an integrated data envelopment analysis (DEA) and analytic hierarchy process (AHP) approach to a multi-hierarchy grey relational analysis (GRA) model. Consistent with the most real-life applications, the authors focus on a two-level hierarchy in which the attributes of similar characteristics can be grouped into categories. Nevertheless, the proposed approach can be easily extended to a three-level hierarchy in which attributes might also belong to different sub-categories and further be linked to categories.

The procedure of incorporating the DEA and AHP methods in a two-level GRA may be broken down into a series of steps. The first three steps are under the heading of attributes and the latter three steps are under the heading of categories as follows: computing the grey relational coefficients of attributes for each alternative using the basic GRA model which further provides the required (output) data for an additive DEA model; computing the priority weights of attributes and categories using the AHP method which provides a priori information on the adjustments of attributes and categories in additive DEA models; computing the grey relational grades of attributes in each category for alternatives using an additive DEA model; converting the grey relational grades of attributes to the grey relational coefficients of categories; computing the grey relational grades of categories for alternatives using an additive DEA model; computing the dissimilarity grades of categories for the tied alternatives using an additive DEA exclusion model.

The proposed approach provides a more reasonable and encompassing measure of performance in a hierarchy GRA, based on which the overall ranking position of alternatives is obtained. A case study of a wastewater treatment technology selection verifies the effectiveness of this approach.

This research is a step forward to overcome the current shortcomings in a hierarchy GRA by extracting the benefits from both the objective and subjective weighting methods.

The purpose of this paper is to evaluate resource configuration and service ability in hospital on public private partnership (PPP) model (Chaonan Minsheng Hospital of Guangdong Province), supplying decision-making reference for participants of hospital on PPP model.

Four model of grey relational analysis (GRA) (Deng's correlation degree, grey absolute correlation degree, grey relative correlation degree and grey comprehensive correlation degree) are applied to evaluate resource configuration and service ability, a total of 11 indicators of hospital on PPP model public hospital and private hospital from 2007 to 2011.

The paper finds that different GRA models have different results when the paper applied them to evaluate resource configuration and service ability in hospital on PPP model. More than 60 per cent indicators of resource configuration (total six indicators) and service ability (total six indicators) are assessed as “hospital on PPP model ≻ public hospital” or “hospital on PPP model≻ private hospital” from three models of Deng's correlation degree, grey absolute correlation degree and grey comprehensive correlation degree.

Evaluation of resource configuration and service ability for hospital on PPP model with GRA makes results quantified objective and provides reference for decision making and management. GRA makes the comparison of resource configuration and service ability between hospital on PPP model and other model hospitals becoming possible.

The shortcoming for data analysis method of “large sample” is overcome and data analysis method of “small sample” is realized by using GRA, which broaden the method of evaluating hospital on PPP model.

The purpose of this paper is to evaluate, analyse and select the best suppliers for Satrec Vitalait Milk Company, operating in Senegal, based on criteria obtained from economic, environmental and social dimensions of sustainable supply chain management, through the application of Deng’s grey relational analysis (GRA) model, absolute GRA model (ADGRA) and a novel second synthetic GRA (SSGRA) model, combined with one decision making under the uncertainty-based model, namely, the Hurwicz criteria.

The research adopts a new synthetic GRA model and highlights its reliability on small sample gathered from four senior experts of the company who administered a total number of 28 specialists operating in four departments of the company, through the employment of a self-administered questionnaire designed based on criteria identified from the literature that were refined via a Q-sort model.

The outcomes of the research methodology designated that all the selected five suppliers present a degree of attaining sustainability due to the fact that supplying unprocessed milk does not require the use of polluting methods for stocking and transportation. The undertaken study specifies that all the socio-environmental criteria play a crucial role in shaping the sustainability level of Satrec Vitalait’s suppliers and demonstrates the accuracy of the results obtained through the second synthetic degree of grey relation analysis for ranking the suppliers. Supplier 2 was found to be the best supplier for the company and, as result, a model for other suppliers to mimic.

Future researchers can replicate the GRA-based supply chain model proposed in the current study in different environments especially in the context of green supply chain. Also, in future the SSGRA model, while using the bidirectional ADGRA instead of the conventional ADGRA, should also be tested, especially when the data sequences associated with different supply chain parameters have inconsistent directions. Also, comparative analysis of SSGRA-based results with that of modern statistical methods like structural equation modelling can also be used for future explorations. Furthermore, the current study is built upon the data associated with the Satrec Vitalait Milk Company (Senegal); therefore, the findings should be generalised with caution.

The study can be seen as a first-stepping stone for gauging and selecting the best sustainable supplier for Satrec Vitalait using grey system theory. For purpose of attaining the research goal, the SSGRA was exploited as an innovative experimental approach to estimate relationships between criteria with regard to the sustainability level of the company’s suppliers. Under this scope, relationships between criteria themselves and their goal were depicted by Deng’s degree of GRA and AGRA, respectively. The research is innovative by means of the framework of its methodology and data analysis.

Seasonal fluctuation interference often affects the relational analysis of economic time series. The main purpose of this paper is to propose a new grey relational model for relational analysis of seasonal time series and apply it to identify and eliminate the influence of seasonal fluctuation of retail sales of consumer goods in China.

First, the whole quarterly time series is divided into four groups by data grouping method. Each group only contains the time series data in the same quarter. Then, the new series of four-quarters are used to establish the grey correlation model and calculate its correlation coefficient. Finally, the correlation degree of factors in each group of data was calculated and sorted to determine its importance.

The data grouping method can effectively reflect the correlation between time series in different quarters and eliminate the influence of seasonal fluctuation.

In this paper, the main factors influencing the quarterly fluctuations of retail sales of consumer goods in China are explored by using the grouped grey correlation model. The results show that the main factors are different from quarter to quarter: in the first quarter, the main factors are money supply, tax and per capita disposable income of rural residents. In the second quarter are money supply, fiscal expenditure and tax. In the third quarter are money supply, fiscal expenditure and per capita disposable income of rural residents. In the fourth quarter are money supply, fiscal expenditure and tax.

This paper successfully realizes the application of grey relational model in quarterly time series and extends the applicable scope of grey relational model.

This paper aims to propose an integration of the analytic hierarchy process (AHP) and data envelopment analysis (DEA) methods in a multiattribute grey relational analysis (GRA) methodology in which the attribute weights are completely unknown and the attribute values take the form of fuzzy numbers.

This research has been organized to proceed along the following steps: computing the grey relational coefficients for alternatives with respect to each attribute using a fuzzy GRA methodology. Grey relational coefficients provide the required (output) data for additive DEA models; computing the priority weights of attributes using the AHP method to impose weight bounds on attribute weights in additive DEA models; computing grey relational grades using a pair of additive DEA models to assess the performance of each alternative from the optimistic and pessimistic perspectives; and combining the optimistic and pessimistic grey relational grades using a compromise grade to assess the overall performance of each alternative.

The proposed approach provides a more reasonable and encompassing measure of performance, based on which the overall ranking position of alternatives is obtained. An illustrated example of a nuclear waste dump site selection is used to highlight the usefulness of the proposed approach.

This research is a step forward to overcome the current shortcomings in the weighting schemes of attributes in a fuzzy multiattribute GRA methodology.

The purpose of this paper is to investigate the relative influences of technical and functional quality levels of service quality and patient satisfaction. In this context, the healthcare service quality and the factors affecting customer satisfaction were evaluated using the grey relational analysis (GRA) method.

This is a survey-based study which involves 15 patients in a dialysis center, so the GRA is applied to clarify the uncertainty on service quality level with a limited number of patients without any statistical distribution. In order to reveal whether service quality and customer satisfaction are two different structures, a GRA model is built with ten different quality factors.

Results show that each quality factor has a different effect on the quality of service. Another important finding is that service quality and customer satisfaction are different structures for customers.

The results enable healthcare managers to understand the importance of patient care and the importance of service quality if they want to facilitate their use of their expectations in related factors.

The study is the first in terms of the application of GRA models in a private health institution operating in Turkey. Successful implementation of the GRA method allows a reasonable decision to be made with a limited number of data at hand. It is considered that the method can be used successfully in other health institutions in the Turkish Health System.

This study aims to explore the effects of the COVID-19 outbreak on exports of goods and services, logistics performance, environmental management system (ISO 14001) certification and quality management system (ISO 9001) certification in top affected Asian countries of India, Iran, Indonesia, Philippines, Bangladesh and Pakistan.

A novel grey relational analysis models’ approach is used to examine the inter-relationship between COVID-19 economic growth and environmental performance. Moreover, the authors applied a conservative (maximin) model to investigate which countries have the least intensifying affected among all of the top affected COVID-19 Asian countries based on the SS degree of grey relation values. The data used in this study was collected from multiple databases during 2020 for analysis.

Results indicate that the severity of COVID-19 shows a strong negative association and influence of COVID-19 on the exportation of goods and services, logistics performance, ISO 9001 and ISO 14001 certifications in all the six highly affected countries during a pandemic outbreak. Although the adverse effects of COVID-19 in exporting countries persisted until December 31, 2020, their magnitude decreased over time in Indonesia and Pakistan. During the COVID-19 outbreak, Pakistan showed comparatively better performance among the six top highly affected Asian countries due to its smart locked down strategy and prevents its economy from severe damages. While India and Iran export drastically go down due to a rapid increase in the number of COVID-19 cases and deaths.

The research findings produce much-required policy suggestions for leaders, world agencies and governments to take corrective measures on an emergent basis to prevent the economies from more damages and improve their logistics, environmental and quality performance during the pandemic of COVID-19.

This study develops a framework and investigates the intensifying effects of COVID-19 effects on economic growth, logistics performance, environmental performance and quality production processes.

Despite the growing importance of online word-of-mouth (WOM) with regard to television (TV) ratings, it is usually excluded from early prediction models. The purpose of this paper is to investigate the role of online WOM in TV ratings predictions, focussing on whether the incorporation of online WOM could improve predictions of TV ratings, and extracts meaningful rules for decision-making.

The author uses online WOM as a potential predictive variable in the TV ratings prediction model. The author matches a list of programs based on TV ratings for the movie channel with internet user reviews and TV ratings information from Yahoo! Movies (YM) and XYZ Company. The data set includes 71 movies, for which the data were analyzed with a hybrid model.

Grey relational analysis shows that online WOM is a useful ex ante determinant of TV ratings. As a predictive variable, it plays an essential role in enhancing TV ratings predictions. The experimental results also indicate that the proposed model surpasses other listed methods in terms of both accuracy and reduction of variables, while the proposed procedure yields a set of easily understandable decision rules that facilitate the interpretation of TV ratings information.

This paper identifies critical predictors of TV ratings and suggests that online WOM messages are a credible source. A hybrid model is developed to illustrate an intelligent prediction system for TV ratings.

The study demonstrates the effectiveness of online WOM and its impact on TV ratings. It offers an intelligent prediction system for TV ratings with practical implications for managers within the TV industry.