Necessary and sufficient conditions for existence of maximal solutions for inf-α composite fuzzy relational equations

On complete Brouwerian lattices, an inf-α composite fuzzy relational equation and its equation system are investigated. In finite domains, a necessary and sufficient solvability condition is proposed for the equation, then all its maximal solutions and the whole solution set are determined. Subsequently, the whole solution set for the equation system is determined. In infinite domains, sufficient conditions for existence of a maximal solution for the equation and the equation system are shown, respectively. Afterwards, a necessary and sufficient condition, that there exists a maximal solution which is more than or equal to any solution, is presented for the equation