Some Conditions Of The Existence Of A Maximal Solution For An @-Fuzzy Relational Equation On A Complete Brouwerian Lattice

In the case of infinite domains,it is proven that there exists a maximal solution X" of A@X = b such that X* ≥ X for every solution X of A@X = b if the solution set of A@X = b is unempty and b has an irredundant completely meet-irreducible decomposition .It is also identified that there exists a maximal solution X* of A@X = B such that X* ≥ X for every solution X of A@X = B if the solution set of A@X = Bis unempty and every component of B is dual-compact and has an irredundant finite-decomposition.In the end, a necssary and sufficient condition that there exists a maximal solution X* of A@X = bsuch that X * ≥ X for every solution X of A@X = b is given when the solution set of A@X = b is unempty.