通过矩阵的半张量积求解模糊双线性方程的最大解和最小解  

Solving Maximum and Minimum Solutions of Fuzzy Bilinear Equations via Semi-tensor Product

作　　者：范洪彪 张智广[1] 许晶 FAN Hong-biao;ZHANG Zhi-guang;XU Jing(School of Mathematics and Big Data,Dezhou University,Dezhou Shandong 253023,China)

机构地区：[1]德州学院数学与大数据学院,山东德州253023

出　　处：《德州学院学报》2022年第2期5-13,共9页Journal of Dezhou University

摘　　要：研究了如何求解模糊双线性方程(FBES)的最大解和最小解问题。首先,讨论了FBE的解的结构;然后,通过矩阵的半张量积(STP)把相关的逻辑方程转化为代数方程。在此基础之上,提出求解FBE的最大解和最小解的方法。最后,给出一个数值算例来表明所得结论的有效性。In this paper, the problem about solving maximum and minimum solutions of fuzzy bilinear equations(FBEs) is investigated. First, the structure of solutions to FBE is researched. Then the logical equations are convertrd into algebraic ones via semi-tensor product(STP) of matrices and the technique of vector expression logical variables. Based on it, the maximum and minimum solutions to FBE are given with the proposed method.Finally, an example is presented to demonstrate the effectiveness of obtained results.

关 键 词：模糊双线性方程 半张量积 多值逻辑 向量表达 

分 类 号：O241.6[理学—计算数学]