The Sufficient and Necessary Condition for the Existence of the Solution of L-Relation Equations T(a, x) = b , I (a, x) = b
Liao Da-jian · 2004
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.