Affiliations: [a] College of Mathematics and Statistics, Northwest Normal University, Lanzhou, PR China | [b] School of Mathematics and Statistics, Longdong University, Qingyang, Gansu, PR China
Correspondence:
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Corresponding author. Zengtai Gong, College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, PR China. E-mail: zt-gong@163.com.
Note: [1] This work is supported by National Natural Science Foundation of China (61763044).
Abstract: As a key theoretical basis of fuzzy analysis, a new representation of the two-dimension fuzzy numbers is proposed in this paper. We also present a new method for solving the fuzzy system of linear equations with the two-dimension fuzzy data based on the new representation of the two-dimension fuzzy numbers, which may translate a fuzzy system of linear equations into two real systems of linear equations, one is an n × n real system of linear equations and the other is a (2n) × (2n) real system of linear equations, where the coefficients, the right hand term and the unknown term of the (2n) × (2n) real systems are all positive real numbers. Accordingly, we compare the classical methods with the technique on the basis of the study of the two-dimensional fuzzy linear system proposed in this paper for an one-dimensional fuzzy linear system, and the results shows that they have the same solutions. Finally, the conditions of the existence of the solutions for a fuzzy system of linear equations are discussed, and the examples are given to show the efficiency and effectiveness of the method investigated in this article.
Keywords: Fuzzy numbers, two-dimension fuzzy numbers, fuzzy linear system, fuzzy
system of linear equations
