Optimization of fuzzy relational equations with max-av composition

Max–min and max-product compositions are commonly utilized to optimize a linear objective function subject to fuzzy relational equations. Both are members in the class of max-t-norm composition. In this study, the max-av composition is considered for the same optimization model, which does not belong to the max-t-norm composition. However, max-av composition generates some properties of the solution set that are similar to the max-product composition. Thanks to these properties, a simple value matrix with rules can be applied to reduce problem size. Thus, this study proposes an efficient procedure for obtaining optimal solutions without decomposing the problem into two sub-problems or finding all the potential minimal solutions.