L-关系方程T(a,x)=b与方程I(a,x)=b有解的充要条件

The Sufficient and Necessary Condition for the Existence of the Solution of L-Relation Equations T(a, x) = b , I (a, x) = b

进一步讨论方程T(a,x)=b与方程I(a,x)=b的解的结构,得到了它们的解集,且得到了它们有解的充分必要条件,并利用方程T(a,x)=b与方程I(a,x)=b的解集研究方程T((a1,a2),(x1,x2))=(b1,b2)以及方程I((a1,a2),(x1,x2))=(b1,b2)的解结构与与解集.还指出文献[1]中一个基本定理的错误.其中L为完备Brouwer格,T为无穷∨-分配伪t 模,I是无穷∧-分配蕴涵算子.

In this paper, we discuss the structure of the solution of equations T(a, x) =b and I(a,x)=b, get the sets of all solutions of them under certain conditions. Besides, the paper obtains the sufficient and necessary condition of the existenceof the solution. After the sets of the solutions of the equations T(a, x)=b and I(a, x) =b, we get the structure and set of all solutions of equation T((a_(1), a_(2)), (x_(1), x_(2))) = (b_(1), b_(2)) and the equation I((a_(1), a_(2)), (x_(1), x_(2))) = (b_(1), b_(2)). Finally, we point out default in some theoremsin paper[1], Where L is a complete Brouweian lattice, T is a infinitely ∨-distributive Pseudo-t-norm, and I is a infinitely ∧-distributive implication.