一类格上的双线性方程

The Bilinear Equations in Some Class of Lattices

文章求出了定义在模糊代数上的双线性方程AX=BX的最大解,本文讨论了定义在更广泛的一类格上的双线性方程AX=BX,得到两个结果:(1)当背景格为有限时,求出方程的全部解;(2)当背景格为无限时,[2]中给出的确定模糊双线性方程的最大解和最大结果的方法可以在这里推广。

In [2], the method to find the largest solution of bilinear equation A_1X=A_2X defined on the fuzzy algebra was given, where A_1, A_2 were matrices and X was an n- dimension vector. In this article, we will discuss the same bilinear eqation defined on some class of lattices. That is of the lattices with first-infinite-distributivity, in which every element can be expressed as a finite join of join-irreducible elements. We obtain following results: 1)when the background lattice is finitd, we find the largest solution of the bilinear equation; 2)when the background lattice is infinite, the method to find the largest solution of the bilinear equation in [2] is generalized here