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This paper attempts to establish the conceptional and computational systems of grey determinant and apply it to solve n grey equations with n grey linear equations, which can be viewed as the important parts of grey mathematics.

Starting from the fact that missing information often appears in complex systems, the true values of elements when constructing a determinant and of coefficients when solving n equations with n linear equations cannot be obtained, so they are uncertain. However, their ranges can be obtained by using correct investigation methods. The uncertain elements and coefficients are grey and their ranges are number‐covered sets. On the basis of the results of Li and Wang, the paper systematically proposes the definition system of grey determinant and n grey linear equations, and utilizes the computational rules of grey determinant to solve the n grey equations with n grey linear equations. Some numerical examples are computed to illustrate the results in this paper.

The results show that the ranges of grey value of grey determinant and grey solutions of grey equations with n grey linear equations can be obtained by using computational rules proposed.

Because the determinant and the linear equations have been widely used in many fields such as system controlling, economic analysis and social management, and the missing information is a general phenomenon for complex systems, grey determinant and grey linear equations may have great potential application in the real world. The method realizes the feasibility of system analysis under uncertain situations.

The paper succeeds in providing systematic results of computation of uncertain determinant and n linear equations by using grey systems theory and enriches the contents of grey mathematics.

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.

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.

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.

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.

To explore a more effective method to study the information content of grey numbers.

An axiomatic approach is used for the measurement of information content of a given grey number.

A new definition for information content of grey numbers is introduced. And, relevant results are proven.

This work fills the vacancy on how to measure the information value contained in a grey number.

We introduce the concepts of information, uncertainty information, systems and uncertainty systems, analyze the intension of these concepts, and point out the differences and connections among various concepts of systems. We put forward a mathematical method to research uncertainty systems and present a problem that can be solved with our method but cannot be solved with the interval analyzing method. Otherwise, from analyzing the purpose of introducing the concepts of information, uncertainty information, systems and uncertainty systems, we conclude that uncertainty information and uncertainty systems are among the most important subjects studied in scientific research, especially in applied research, both that being presently conducted and the abundance which is to come in the future.

The purpose of this paper is to propose an extending correlation analysis method to deal with the correlation analysis between the sequences with incomplete information.

Based on the axiomatic definition of a grey number and its greyness degree in grey system theory, the whitenization mean, whitenization difference, whitenization covariance of sequences with interval grey numbers and their greyness degrees are defined in turn. In addition, the whitenization correlation coefficient and its greyness degree of sequences with interval grey numbers are also defined. By using the relationship between the greyness degree and kernel for a grey number, the transformation formula from the whitenization value and greyness degree of correlation coefficient to form of interval grey numbers are put forward further.

The whitenization value of correlation coefficient efficient of two arbitrary sequences with interval grey numbers have symmetry, with same greyness degree but without normalization in the interval [−1, 1]; the mean, difference, covariance and correlation coefficient defined in statistics are all the special cases of those in sequences with interval grey numbers.

Due to the complexity of operation of grey numbers, the reliability of correlation coefficient of interval numbers sequence is difficult to be tested by constructing statistics at present. The further research is needed.

The correlation analysis method of interval grey numbers can contribute to the further researches on the incomplete information system in the real world.

On the basis of grey system theory, a correlation analysis method for analyzing information incomplete sequences is proposed.

The purpose of this paper is to propose a new grey system model used for prediction.

It had been proven that the GM(1,1) model is a biased exponential model, the model is fit for non‐negative raw data, which accord with or basically accord with the exponential form and do not have a quick growth rate. Based on the results, an unbiased GM(1,1) model was proposed. With the method of transforming every datum of raw data sequence into its 2‐th root, a new data sequence from the raw data sequence can be produced. The new data sequence is used to establish an unbiased GM(1,1) model and statistical experiments and a practical example in load forecasting are given in the paper.

The results of statistical experiments and a practical example in load forecasting show the proposed method is effective in increasing the accuracy of the model.

The model exposed in the paper can be used for constructing models of prediction in many fields such as agriculture, electric power, IT, transportation, economics, management, etc.

The paper succeeds in proposing a modified unbiased GM(1,1) model that has high accuracy. The model is applied to the field of load forecasting and the results show the model is better than the unbiased GM(1,1) model. The model proposed has great theoretical and practical value.