一类格上的双线性方程

The Bilinear Equations in Some Class of Lattices

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