Solution sets of inf-αTinf-αT fuzzy relational equations on complete Brouwerian lattices

This work studies the problem of solving a fuzzy relational equation with inf-αTinf-αT composition on a complete Brouwerian lattice, where TT is a pseudo-t  -norm. Two necessary and sufficient conditions that solution sets are nonempty are obtained. When TT is normal and the solution set of the equation is nonempty, a sufficient condition that there exists maximal solutions is given. Further, the solution set of the equation is presented.