Covered solution for a grey linear program based on a general formula for the inverse of a grey matrix

• Published in: Grey systems Vol. 4; no. 1; pp. 72 - 94
• Main Authors: Li, Qiao-Xing, Liu, Sifeng, Wang, Nai-Ang
• Format: Journal Article
• Language: English
• Published: Bingley Emerald Group Publishing Limited 28.01.2014
• Subjects: Algorithms; Applied mathematics; Fuzzy logic; Fuzzy sets; Grey systems; Information & knowledge management; Information systems; Linear programming; Mathematical models; Operations research; Production management; Random variables; Studies; System theory; Poor information; Grey linear programming; Matrix-covered set; Grey system theory; Grey mathematics; Grey matrix
• ISSN: 2043-9377; 2043-9385
• DOI: 10.1108/GS-10-2013-0023

Purpose – 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. Design/methodology/approach – 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. Findings – 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. Practical implications – 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. Originality/value – 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.