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

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.