【摘要】 坡代数是一类积不超过其因子的加法幂等半环,它概括了布尔代数、模糊代数和有界分配格。本文定义了整坡代数上的秩-1矩阵的周长是其左、右因子的非零元素之和,并给出了其上的秩-1矩阵和的周长所满足的不等式,获得了保持其周长的算子,这概括和发展了布尔矩阵、模糊矩阵上的相关结论。更多还原

【Abstract】 Inclines are the additively idempotent semirings in which products are less than or equal to factors.They generalize Boolean algebra,fuzzy algebra and distributive lattice.This paper defines that the perimeter of rank-1matrices over inclines is the sum of nonzero elements of its left and right factors,and proves the inequality about the perimeter of the sum of rank-1matrices over inclines and gives the preserving operators of rank-1matrices over inclines.The results in the present paper generalize and develop correlated results over Boolean matrices and fuzzy matrices.更多还原