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This paper attempts to establish the general formula for computing the inverse of grey matrix, and the results are applied to solve grey linear programming. The inverse of a grey matrix and grey linear programming plays an important role in establishing a grey computational system.

Starting from the fact that missing information often appears in complex systems, and therefore that true values of elements are uncertain when the authors construct a matrix, as well as calculate its inverse. However, the authors can get their ranges, which are called the number-covered sets, by using grey computational rules. How to get the matrix-covered set of inverse grey matrix became a typical approach. In this paper, grey linear programming was explained in detail, for the point of grey meaning and the methodology to calculate the inverse grey matrix can successfully solve grey linear programming.

The results show that the ranges of grey value of inverse grey matrix and grey linear programming can be obtained by using the computational rules.

Because the matrix and the linear programming 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 matrix and grey linear programming may have great potential application in real world. The methodology realizes the feasibility to control the complex system under uncertain situations.

The paper successfully obtained the ranges of uncertain inverse matrix and linear programming by using grey system theory, when the elements of matrix and the coefficients of linear programming are intervals and the results enrich the contents of grey mathematics.

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 propose the input‐occupancy‐output analysis for grey situations and to manage the economic systems with missing information. The situation is realistic in practice.

During the decision‐making process of an economic system, the managers often get some uncertain data for the missing information. Then, it becomes difficult to analyze the complex system by using the input‐occupancy‐output analysis. Since the uncertain data are grey numbers, the decision maker can control it by using grey system theory and the input‐occupancy‐output analysis.

Get the grey direct consumption and occupancy coefficient matrices and the computational formulas of their matrix‐covered sets. The grey model of input‐occupancy‐output analysis and its covered solution are also obtained.

The chaos of the grey statistic data should satisfy a level of accuracy and it is key to get the number‐covered set that the true data belongs to.

A feasible approach to control the economic system that the accurate data are difficult to be obtained.

Give a new approach to study an economic system by using grey system theory.

The purpose of this paper is to explain the connotation of grey number, which is the basic unit of grey mathematics and the key to establish the mathematic framework of grey system theory.

From the grey hazy set, the paper re‐defines grey number and the operation of grey‐number element, then some properties are obtained. Based on them, the operation of grey‐matrix element is given. The general definition of grey function and its operation are also proposed.

The connotation of grey number is elaborated and the elementary framework of grey mathematics can be established.

The researched object, objective and techniques of grey system theory have not been logically proposed and they may influence the comprehension of grey system theory. The obtained results of grey mathematics may significantly promote its development.

The paper can enable managers to control the complex system with missing information by using the quantitative approaches.

Grey mathematics may become a branch of mathematics to deal with proximate calculation.