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This paper aims to resolve the uncertain problem in suppliers selection chain management system through using the proposed multiple attribute decision‐making (MADM) approach.

The approach which combines grey system theory with rough set theory is proposed.

This proposed approach take advantage of mathematical analysis power of grey system theory and at the same time take advantage of data mining and knowledge discovery power of rough set theory. It will be suitable to decision making under a more uncertain environment.

Provides a viewpoint on the attribute values and attribute weights of rough set decision table for all alternatives are decided by grey number based on grey system theory. The best ideal supplier can be decided by grey relational analysis based on grey number.

The purpose of this paper is to summarize the advances in grey system theory research and various application achievements in science and engineering. At the same time, it commemorates the 40th anniversary of the birth of grey system theory and the 10th anniversary of Grey Systems–Theory and Application.

Firstly, the innovations of theoretical research in grey system theory were summarized and some of the widely recognized new results are briefly described. By searching and combing the research results of grey system theory in China national knowledge infrastructure (CNKI) database and Web of Science by Institute for Scientific Information (ISI), this paper shows the rapid development trend of grey system theory in the past 40 years, and the successful applications of grey system theory in the fields of social sciences, natural sciences and engineering technologies.

More than 227 thousands literature were found by input 10 phrases such as grey system, grey number and sequence operator etc. in CNKI database. After entering the new century, the number of grey system papers included in CNKI database is increasing rapidly. Since 2008, more than 10 thousands papers have been included per year and more than 15 thousands papers have been included per year since 2014. Grey system method and model are widely used in physics, chemistry, biology and other fields of natural science, as well as transportation, electric power, machinery and other fields of engineering technology, and a large number of valuable results have been achieved.

It can be seen that the grey system theory plays an important role in promoting China’s scientific and technological progress, innovation and development and high-level talent training from tens of thousands of literatures marked with important national science and technology projects and a large number of grey system literatures published by China’s double first-class universities and double first-class discipline construction universities.

Both innovations of theoretical research and practical application play important role in the growth of new theory. The innovations of theoretical research provide methods and tools for practical application, which is conducive to improve application efficiency and broaden application fields. A large number of practical applications needs have become the source of theoretical innovation and the solid background for the birth of theoretical innovation achievements.

In order to more accurately predict the dynamics of the e-commerce market and increase the comprehensive value of the circular e-commerce industry, proposes to use Grey system theory to analyze the circular economy of the e-commerce market.

Construct a Grey system theory model, analyze the big data of e-commerce and circular economy of the e-commerce market and predict the development potential of China's e-commerce market.

The results show that the Grey system theory model can play an important role in the data analysis of circular economy of the e-commerce market.

Use Grey model to analyze e-commerce data, discover e-commerce market rules and problems and then optimize e-commerce market.

In the current customer-driven market, the manufacturers have to be highly responsive and flexible to deliver a variety of products. Hence, to meet this dynamic and uncertain market changes, the production system, which enables the manufacturing of such variety of products should be able to meet such diverse, dynamic changes. Hence, selecting a suitable manufacturing system is a key strategic decision for today's manufacturing organization, which needs to survive in these uncertain market conditions. Hence, the purpose of this paper is to present a decision-making model for selecting the best manufacturing system and also discuss the criteria on the basis of which the management can select the same.

A case of small- and medium-sized company is presented, in which the management is deciding to establish a most suitable manufacturing system. To supplement this, a suitable multi-criteria decision-making model (MCDM), the grey approach is used to analyze manufacturing system alternatives based on various decision criteria to arrive a comparative ranking.

An extensive analysis of grey-based decision-making model described grey decision matrix, grey normalized decision matrix, grey weighted normalized decision matrix and grey possibility degrees for three alternatives revealed that lean manufacturing systems was found to be the most suitable manufacturing system among three alternatives for a given case.

The same study can be extended by including sub-criteria with main criteria for selection of manufacturing system by utilizing two MCDM techniques such as AHP or ANP with Grey approach.

The Grey approach has been discussed in a detailed way and it will be useful for the managers to use this approach as a tool for solving similar type of decision-making problems in their organizations in the future.

Although, the problem of selecting a suitable manufacturing system is often addressed both in practice and research, very few reports are available in the literature of Grey-based decision models that demonstrated its application for selecting a suitable manufacturing systems.

The purpose of this paper is to introduce the elementary concepts and fundamental principles of grey systems and the main components of grey systems theory. Also to discuss the astonishing progress that grey systems theory has made in the world of learning and its wide‐ranging applications in the entire spectrum of science.

The characteristics of unascertained systems including incomplete information and inaccuracies in data are analysed and four uncertain theories: probability statistics, fuzzy mathematics, grey system and rough set theory are compared. The scientific principle of simplicity and how precise models suffer from inaccuracies are also shown.

The four uncertain theories, probability statistics, fuzzy mathematics, grey system and rough set theory are examined with different research objects, different basic sets, different methods and procedures, different data requirements, different emphasis, different objectives and different characteristics.

The scientific principle of simplicity and how precise models suffer from inaccuracies are shown. So, precise models are not necessarily an effective means to deal with complex matters, especially in the case that the available information is incomplete and the collected data inaccurate.

The elementary concepts and fundamental principles of grey systems and the main components of grey systems theory are introduced briefly. The reader is given a general picture of grey systems theory as a new method for studying problems where partial information is known, partial information is unknown; especially for uncertain systems with few data points and poor information.

The purpose of this paper is to present the scientific background from which grey systems theory came into being, the astonishing progress that grey systems theory has made in the world of learning and its wide‐ranging applications in the entire spectrum of science.

The grey uncertainty is compared with other kinds of uncertainty such as stochastic uncertainty, unascertainty, fuzzy and rough uncertainty.

The advances in grey systems theory and its various successful applications are introduced individually by algorithms of grey numbers and grey algebraic systems, grey dynamic models and grey predictions, grey optimization analysis for decision making, grey control models.

Many scientific theories require the unremitting efforts of several generations of people and have gone through hundreds of years before reaching maturity and perfection. Grey systems theory is still in its growth period. So, it is unavoidable that there exist immature and imperfect parts in the theory.

Grey systems theory is a new method for studying problems of uncertainty with few data points and poor information. This new theory studies small samples and systems with poor information, which have partial information known, partial information unknown. It describes adequately and monitors effectively systems' operations and evolutions through extracting valuable information from the little known information. Grey systems theory comes into being along with the development of modern systems science and uncertainty systems theories and methods. It is also a result of deepened perceptivity about uncertain systems.

During the service period of communication satellite systems, their performance is often degraded due to the depletion mechanism. In this paper, the grey system theory is applied to the multi-state system effectiveness evaluation and the grey Lz-transformation ADC (availability, dependability and capability) effectiveness evaluation model is constructed to address the characteristics of the communication satellite system such as different constituent subsystems, numerous states and the inaccuracy and insufficiency of data.

The model is based on the ADC effectiveness evaluation method, combined with the Lz transformation and uses the definite weighted function of the three-parameter interval grey number as a bridge to incorporate the possibility of system performance being greater than the task demand into the effectiveness solution algorithm. At the same time, using MATLAB (Matrix laboratory) to solve each state probability, the same performance level in the Lz transform is combined. Then, the system effectiveness is obtained by Python.

The results show that the G-Lz-ADC model constructed in this paper can accurately evaluate the effectiveness of static/dynamic systems and certain/uncertain system and also has better applicability in evaluating the effectiveness of the multi-state complex system.

The G-Lz-ADC effectiveness evaluation model constructed in this paper can effectively reduce the complexity of traditional effectiveness evaluation models by combining the same performance levels in the Lz-transform and solving the effectiveness of the system with the help of computer programming, providing a new method for the effectiveness evaluation of the complex MSS. At the same time, the weaknesses of the system can be identified, providing a theoretical basis for improving the system’s effectiveness.

The possibility solution method based on the definite weighted function comparing the two three-parameter interval grey numbers is constructed, which compensates for the traditional calculation of the probability based on numerical values and subjective preferences of decision-makers. Meanwhile, the effectiveness evaluation model integrates the basic theories of three-parameter interval grey number and its definite weighted function, Grey−Markov, grey universal generating function (GUGF), grey multi-state system (GMSS), etc., which is an innovative method to solve the effectiveness of a multi-state instantaneous communication satellite system.

As the grey systems theory has been used over the time in different economic areas, in the following, a short literature review will be put forward, starting from the usage of these theory in the supply chain management, decision-making process, financial performance evaluation, credit risk, energy consumption, investment efficiency, etc. The purpose of this paper is to identify some key studies from all the economic areas in which the grey systems can be used in order to open and to bring to the researchers new domains in which they can manifest their interest and in which they can successfully use the methods offered by the grey systems theory.

Using the search engine offered by the Web of Science, a literature review has been performed for the economic grey systems applications developed over the time on both economic diagnosis and system’s forecasting. In addition, some hybrid grey systems theory – artificial intelligence techniques models have also been presented.

The grey systems theory has brought its contribution to numerous economic application from various fields such as: supply chain management, decision-making process, financial performance evaluation, credit risk, energy consumption, investment efficiency, firms’ bankruptcy, product development, consumer income, monetization ratio, etc.

The present paper identifies the some of the most representative examples in which the grey theory 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.

Unlike other review papers written on the grey systems theory area, the present paper is only focusing on the economic applications in which this theory has been successfully used, bringing to the reader a general overview on this field and, in the same time, enabling new research perspectives.

The purpose of this paper is to discuss how tacit and explicit knowledge determine grey knowledge and how these are stimulated through interactions within networks, forming the grey hybrid intelligent systems (HISs). The feedback processes and mechanisms between internal and external knowledge determine the apparition of grey knowledge into an intelligent system (IS). The extension of ISs is determined by the ubiquity of the internet but, in our framework, the grey knowledge flows assure the viability and effectiveness of these systems.

Some characteristics of the Hybrid Intelligent Knowledge Systems are put forward along with a series of models of hybrid computational intelligence architectures. More, relevant examples from the literature related to the hybrid systems architectures are presented, underlying their main advantages and disadvantages.

Due to the lack of a common framework it remains often difficult to compare the various HISs conceptually and evaluate their performance comparatively. Different applications in different areas are needed for establishing the best combinations between models that are designed using grey, fuzzy, neural network, genetic, evolutionist and other methods. But all these systems are knowledge dependent, the main flow that is used in all parts of every kind of system being the knowledge. Grey knowledge is an important part of the real systems and the study of its proprieties using the methods and techniques of grey system theory remains an important direction of the researches.

The paper discusses the differences among the three types of knowledge and how they and the grey systems theory can be used in different hybrid architectures.

The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new framework of grey system theory.

The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three-dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well.

The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper.

A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate.

The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section.