用二值矩阵表示研究格矩阵的{1}-广义逆和{1,2}-广义逆  

A Study of {1}-generalized Inverses and {1,2}-generalized Inverses of Lattice Matrices with Binary Matrix Representation

作　　者：张丽梅[1] 赵建立[1] 乔立山[1] ZHANG Li—mei;ZHAO Jian—li;QIAO Li—shan(School of Mathematical Sciences,Liaoeheng University,Liaocheng 252059,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《模糊系统与数学》2009年第3期35-41,共7页Fuzzy Systems and Mathematics

基　　金：山东省自然科学基金资助项目(2004ZX13)

摘　　要：用二值矩阵表示的方法(即将格矩阵表示成二值矩阵的线性组合)研究了分配格上矩阵的{1}-广义逆和{1,2}-广义逆。讨论了{1}-广义逆和{1,2}-广义逆存在的充分必要条件。给出了判断这些逆是否存在且存在时找出所有这些逆的算法。从而解决了Kim和Roush(K.H.Kim,F.W.Roush.Generalized fuzzymatrix.Fuzzy Sets and Systems,1980,4(3):293~315)Y2.部分解决了Cao和Kim(Z.Q.Cao,.H.Kim.F.W.Roush.Incline algebraand applications.NewYork:JohnWiley,1984)提出的问题。The{1}-generalized inverses and{1,2}-generalized inverses over distributive lattices are studied using the binary matrix representation technique(i,e.,a lattice matrix can be expressed as a linear combination of some binary matrices).Some necessary and sufficient conditions for the existence of{1}-generalized inverses and{1,2}-generalized inverses are discussed.Furthermore,algorithms are given to test the existence of these generalized inverses and find all of them when they exist.Accordingly,the problems proposed by Kim and Roush(K.H.Kim,F.W.Roush.Generalized fuzzy matrix.Fuzzy Sets and Systems,1980,4(3):293-315)and by Cao and Kim(Z.Q.Cao,K.H.Kim,F.W.Roush.Incline algebra and applications.New York:John Wiley,1984)are solved completely and partly,respectively.

关 键 词：分配格 二值矩阵表示 {1}-广义逆 {1 2}-广义逆 

分 类 号：O152[理学—数学]