| 用二值矩阵表示研究格矩阵的{1}-广义逆和{1,2}-广义逆 |
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| 引用本文： | 张丽梅,赵建立,乔立山.用二值矩阵表示研究格矩阵的{1}-广义逆和{1,2}-广义逆[J].模糊系统与数学,2009,23(3). |
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| 作者姓名： | 张丽梅 赵建立 乔立山 |
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| 作者单位： | 聊城大学,数学科学学院,山东,聊城,252059 |
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| 基金项目： | 山东省自然科学基金资助项目 |
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| 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 fuzzy matrix. Fuzzy Sets and Systems,1980,4(3):293～315)及部分解决了Cao和Kim(Z.Q.Cao,K.H.Kim,F.W.Roush. Incline algebra and applications. New York:John Wiley,1984)提出的问题.
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| 关 键 词： | 分配格 二值矩阵表示 {1}-广义逆 {1 2}-广义逆 |
A Study of {1}-generalized Inverses and {1,2}-generalized Inverses of Lattice Matrices with Binary Matrix Representation |
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| ZHANG Li-mei,ZHAO Jian-li,QIAO Li-shan.A Study of {1}-generalized Inverses and {1,2}-generalized Inverses of Lattice Matrices with Binary Matrix Representation[J].Fuzzy Systems and Mathematics,2009,23(3). |
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| Authors: | ZHANG Li-mei ZHAO Jian-li QIAO Li-shan |
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| Institution: | School of Mathematical Sciences;Liaocheng University;Liaocheng 252059;China |
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| Abstract: | 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 proble... |
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| Keywords: | Distributive Lattice Binary Matrix Representation {1}-generalized inverse {1 2}-generalized Inverse |
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