The definition system and computational rule of grey determinant and its application to n grey equations with n grey linear equations

Citation

Li, Q.-X. (2014), "The definition system and computational rule of grey determinant and its application to n grey equations with n grey linear equations", Grey Systems: Theory and Application, Vol. 4 No. 1. https://doi.org/10.1108/GS-02-2014-001

The definition system and computational rule of grey determinant and its application to n grey equations with n grey linear equations

Article Type: 2013 Awards for Excellence From: Grey Systems: Theory and Application, Volume 4, Issue 1

Qiao-Xing Li, Nai-Ang Wang and Shi-Cheng Chen
Lanzhou University, Lanzhou, People’s Republic of China

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

Keywords: Grey determinant, Grey linear equations, Grey mathematics, Grey systems theory, Linear algebra, Mathematical modelling, Missing information, Number-covered set

“Establishing green supplier appraisement platform using grey concepts”

Nitin Kumar Sahu, Saurav Datta and Siba Sankar Mahapatra

This article originally appeared in Volume 2 Number 3, 2012, Grey Systems: Theory and Application

“A multi-objective programming approach to solve grey linear programming”

Seyed Hossein Razavi Hajiagha, Hadi Akrami and Shide Sadat Hashemi

This article originally appeared in Volume 2 Number 2, 2012, Grey Systems: Theory and Application

“Generalized discrete GM (1,1) model”

Tianxiang Yao, Jeffery Forrest and Zaiwu Gong

This article originally appeared in Volume 2 Number 1, 2012, Grey Systems: Theory and Application

Outstanding reviewers

Dr Jie Cui

Huai Yin Institute of Technology, China

Professor Guo-Dong Li

Tokyo Metropolitan Institute of Technology, Japan