One simple procedure to find the best approximate solution for fuzzy max-average inverse relation

Fuzzy relational equations have played an important role in fuzzy modeling and applied to many practical problems. Most theories of fuzzy relational equations based on a premise that the solution set is not empty. However, this is often not the case in practical applications. Recently, Chakraborty et al, presented an efficient algorithm to solve the best approximate solution for the fuzzy relational equations, X o A = I, with max-min composition, where I denotes the identity matrix. In this paper, some theoretical results of the fuzzy relational equations with max-average composition are proposed for this particular problem. One simple procedure finds the best approximate solution for the discussed problem. A numerical example is provided to illustrate the procedure.