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The purpose of this paper is to attempt to realize a distribution network optimization in supply chain using grey systems theory for uncertain information.

There is much uncertain information in the distribution network optimization of supply chain, including fuzzy information, stochastic information and grey information, etc. Fuzzy information and stochastic information have been studied in supply chain, however grey information of the supply chain has not been covered. In the distribution problem of supply chain, grey demands are taken into account. Then, a mathematics model with grey demands has been constructed, and it can be transformed into a grey chance‐constrained programming model, grey simulation and a proposed hybrid particle swarm optimization are combined to resolve it. An example is also computed in the last part of the paper.

The results are convincing: not only that grey system theory can be used to deal with grey uncertain information about distribution of supply chain, but grey chance‐constrained programming, grey simulation and particle swarm optimization can be combined to resolve the grey model.

The method exposed in the paper can be used to deal with distribution problems with grey information in the supply chain, and network optimization results with a grey uncertain factor could be helpful for supply chain efficiency and practicability.

The paper succeeds in realising both a constructed model of the distribution of supply chain with grey demands and a solution algorithm of the grey mathematics model by using one of the newest developed theories: grey systems theory.

The purpose of this paper is to realize a location‐routing network optimization in reverse logistics (RL) using grey systems theory for uncertain information.

There is much uncertain information in network optimization and location‐routing problem (LRP) of RL, including fuzzy information, stochastic information and grey information, etc. Fuzzy information and stochastic information have been studied in logistics, however grey information of RL has not been covered. In the LRP of RL, grey recycling demands are taken into account. Then, a mathematics model with grey recycling demands has been constructed, and it can be transformed into grey chance‐constrained programming (GCCP) model, grey simulation and a proposed hybrid particle swarm optimization (PSO) are combined to resolve it. An example is also computed in the last part of the paper.

The results are convincing: not only that grey system theory can be used to deal with grey uncertain information about location‐routing problem of RL, but GCCP, grey simulation and PSO can be combined to resolve the grey model.

The method exposed in the paper can be used to deal with location‐routing problem with grey recycling information in RL, and network optimization result with grey uncertain factor could be helpful for logistics efficiency and practicability.

The paper succeeds in realising both a constructed model about location‐routing of RL with grey recycling demands and a solution algorithm about grey mathematics model by using one of the newest developed theories: grey systems theory.

Grey set is the important foundation of the grey mathematics and grey system theory, and the possibility function is the way of expressing grey set. This paper aims to establish the method of determining the possibility function of grey set and discusses its extended applications.

First, the grey kernel and the grey support set of grey set are defined, and the properties of grey kernel are analyzed. Second, according to the decomposition theorem of grey set, a method of determining the possibility function of grey set is put forward in this paper, which is called the method of increasing information and taking maximum and minimum (IITMM), and then it is further simplified as the method of increasing information and taking maximum (IITM), and an simple example is given to illustrate the calculation procedure. Finally, the grey information cluster method (GICM) based on IITM is proposed and applied to the ecological and geographical environment analysis of pine caterpillar.

The results show that the grey kernel of grey set still has grey uncertainty; the method of IITM has simple calculation and strict mathematical basis, and it can synthesize the information of the research object and accords with the principle of using minimum information; the GICM and the fuzzy cluster method have the same classification effect.

The researches show that method of IITM can be used not only to determine the possibility function of the grey set effectively, but also be used for the evaluation and cluster analysis of connotative objects. The classification result of the GICM presented in this paper is more precise than that of the fuzzy cluster method.

The paper succeeds in realizing both the IITM method for determining the possibility function of grey set and the GICM based on IITM for the connotative objects.

Considering current development of Grey Systems Theory (GST), we can come up with the following thesis: practical applications are a dominant subject of research. Thus, what seems to be symptomatic for relatively young knowledge disciplines, the authors observe the presence of imbalance between the development of GST application tools and theory’s epistemological and methodological background. As for GST, epistemological and methodological problems are becoming visible especially in the issues of determining a clear criterion of demarcation of this kind of a theory from others. In other words, this problem can be reduced to the issue of a precise determination of what the category of a grey system and grey information is. This problem is of great importance for further development and popularisation of GST in the world of science. Realising its significance, the purpose of this paper is to create a general overview of Grey Systems epistemology and afterwards create axiomatic and formal frames for a category of greyness.

In order to achieve set goals, two research approaches were accepted. In the area of inference about epistemology of GST an approach characteristic of an analytical philosophy was used, whereas in the case of axiomatic and formal frames for a category of greyness the authors referred to terms of a set theory and the principles of a pragmatic logic.

The result of research is to formulate a concept of a grey system and a concept of grey information in the context of a process of cognition. Moreover, a function of greyness and other fundamental categories of GST will be defined in an axiomatic way.

The paper presents a new consistent frame for the issues of methodological and epistemological backgrounds of GST. An original concept is to refer in considerations to a newly proposed grey space. This space was used for a formal justification of such elementary categories as grey numbers, a weight function of whitenization or grey sequences. The value of achievements shown in the paper is underlined by the fact that proposed theoretical constructions require further development and they can potentially open up new research trends in the GST.

The purpose of this paper is to propose an uncertainty representation and information measurement method for characterizing grey numbers, estimating their internal laws and solving how to generate them based on available information data in the real world.

This paper attempts to present a new mathematical methodology in the field of grey numbers. The generalized grey number is defined at first with the concept of information elements and information samples. Then, the probability function of a grey number is proposed to describe the internal law of the grey number. By finding the feasible information elements from information samples, the probability calculation method for the true value of a grey number is presented. Finally, some numerical examples and comparisons are carried out to assess the efficiency and performance.

The results show that the uncertainty representation and information measurement method is effective in characterizing and quantifying grey numbers based on available information data.

Uncertain information is widespread in practical applications. In this manuscript, the grey number is represented and its information is measured through some existing data in discrete or interval forms, which provides a grey information concept that utilizes information elements to represent uncertainty in the real world.

The proposal presents a novel data-driven method to generate a grey number representation from available data rather than the classical whitening weight function constructed from experience, and the dynamic evolution process of a grey number is measured by the increase of information samples.

The purpose of this paper is to research attribute reduction and decision making by gray dual‐information, taking into account the attribute reduction of attribute decision unknown for the interval gray numbers.

The authors obtain the attribute weights considering the consistency of experts’ judgment matrixes and the decision matrixes with gray information. They propose some experts’ attribute reduction ideas based on interval gray numbers of rough set. With the help of experts’ decision information, they consider attribute uncertainty ratio and attribute value ratio to reduce attribute. Finally, a numerical example shows its feasibility.

Some experts’ attribute reduction ideas are proposed based on interval gray numbers of rough set. With the help of experts’ decision information, attribute uncertainty ratio and attribute value ratio to reduce attribute can be considered.

Attribute reduction is keeping classified information systems under the same conditions and deleting redundant and irrelevant or unimportant attributes in order to solve the problem of decision making. This paper considers the attribute reduction based on gray dual‐information.

The purpose of this paper is to construct a novel grey dominance variable precision rough model.

To deal with the problems that the attribute values of the decision-making object are often not exact numbers but interval grey numbers, and the decision-making attributes satisfy a certain preference relationship in the decision-making information because of the complexity and uncertainty of the real world, the authors take advantage of the theoretical thinking of the grey systems, dominance rough set theory and variable precision rough set theory, and construct a novel dominance variable precision rough set model. On the basis of the thinking logic of grey systems, the authors first define the concepts of balance degree, dominance degree and inferior degree, and then the grey dominance relationship based on the comparison of interval grey numbers. Then the authors use the grey dominance relationship to substitute for the indiscernibility relationship of the variable precision rough set so that the grey dominance variable precision rough model is naturally utilized to reduce the system's attributes in order to derive the needed decision rules. At the end, the authors use a decision-making example of the radar target selection to demonstrate the feasibility and effectiveness of the novel model.

The results show that the proposed model possesses certain fault tolerance ability and can well-realize decision rule extraction and knowledge discovery out of a given incomplete information system.

The method exposed in the paper can be used to deal with the decision-making problems with the grey information, preference information and noise data.

The paper succeeds in realizing both the grey decision-making information with preference information and noise data and the extraction of decision-making rules.

The purpose of this paper is to summarize the different types of grey information, explain the mechanism of grey system modeling and reconstruct the framework of grey system theory (GST).

GST has been developed for more than three decades; however, the framework of GST is still in an evolutionary process. This manuscript first explains grey information in detail, and then summarizes a series of grey system models under limited data and poor information. Figures and general steps for different types of grey system models are provided in this paper.

The findings in this paper clearly differentiate between grey information and other uncertainty information. The differences between grey system models and other uncertainty models are clearly explained. In addition, general steps for different grey system models are given which demonstrate the orientation of grey system modeling.

Theoretical framework is very important for developing a new theory. This paper clarified grey information and grey system-based modeling mechanism. It is very useful to understand and explain the systematic framework of GST and it contributes undoubtedly to make GST perfect.

Grey information is explained in terms of limited data and two types of grey numbers. Accordingly, all of the grey system models were divided into limited data-based grey system models and grey number-based grey system models.

The purpose of this paper is to construct a prediction model of three-parameter interval grey number based on kernel and double information domains to expand the modeling object of grey prediction model from interval grey number to three-parameter interval grey number.

First, the study decomposes the grey valued interval into upper and lower cells with the “center of gravity” as the dividing point and defines the upper and lower information domains of the three-parameter interval grey number. Second, it calculates the kernel, the upper and lower information domains of the three-parameter interval grey number. Then, it constructs the prediction model for kernel sequence and upper and lower information domain sequences, respectively. By deducing the time response expressions of “center of gravity”, lower and upper limits of three-parameter interval grey number, a prediction model of three-parameter interval grey number based on kernel and double information domains is obtained.

This paper provides a prediction model of three-parameter interval grey number based on kernel and double information domains, and the example analysis shows that the method proposed in this paper has higher prediction accuracy and practicality.

In this paper, the modeling object of grey prediction model is extended to the three-parameter interval grey number, so it can be used for the prediction of uncertainty problems, such as stock changing trend, temperature and so on.

By decomposing the grey valued interval into upper and lower cells with the “center of gravity” as the dividing point, gives the definition of upper and lower information domains and then obtains a new method for whitening the three-parameter interval grey number.

The purpose of this study is to construct a gray relational model based on information diffusion to avoid rank reversal when the available decision information is insufficient, or the decision objects vary.

Considering that the sample dependence of the ideal sequence selection in gray relational decision-making is based on case sampling, which causes the phenomenon of rank reversal, this study designs an ideal point diffusion method based on the development trend and distribution skewness of the sample information. In this method, a gray relational model for sample classification is constructed using a virtual-ideal sequence. Subsequently, an optimization model is established to obtain the criteria weights and classification radius values that minimize the deviation between the comprehensive relational degree of the classification object and the critical value.

The rank-reversal problem in gray relational models could drive decision-makers away from using this method. The results of this study demonstrate that the proposed gray relational model based on information diffusion and virtual-ideal sequencing can effectively avoid rank reversal. The method is applied to classify 31 brownfield redevelopment projects based on available interval gray information. The case analysis verifies the rationality and feasibility of the model.

This study proposes a robust method for ideal point choice when the decision information is limited or dynamic. This method can reduce the influence of ideal sequence changes in gray relational models on decision-making results considerably better than other approaches.