【摘要】 针对广义模糊矩阵(即半环及特殊半环上矩阵)的性质问题,采用在路代数(路代数是加法幂等的半环,包括了布尔代数、模糊代数、分配格及斜坡)上定义单增矩阵A≤A2的方法,获得了单增矩阵的构造性质及幂的收敛性质,其中路代数上单增矩阵的幂收敛指数比以往格矩阵幂收敛指数要低,起到了降阶的作用,且将格及斜代数上矩阵的构造问题推广到了路代数上.研究结果推广和完善了格及斜代数上矩阵的相应性质.更多还原

【Abstract】 In view of the property of generalized fuzzy matrix(namely semiring and special semiring matrix), this paper obtained the convergence and the composition of the increasing matrix(A≤A2) in terms of the method of defining increasing matrix over path algebra which is an additively idempotent semiring and it includes Boolean algebra, fuzzy algebra, distributive and incline. Based on these properties, the convergent index of the increasing matrix of path algebra is smaller than the of lattice matrix’s, which plays a role of reducing order, and some properties of compositions of lattice and incline matrices are extended to the matrices of path algebras. So the results obtained in this study generalize and develop the corresponding properties of the lattice matrix and the incline matrix.更多还原