Minimizing a Linear Objective Function under a Max-t-norm Fuzzy Relational Equation Constraint

In this paper minimizing a linear objective function subject to a continuous max-i-norm fuzzy relational equation is considered. Our contributions are two folds. First, We show that this optimization problem can be divided into two subproblems by separating the decision variables associated with negative and nonnegative coefficients in the objective function. A 0-1 integer programming problem as an equivalent model can be derived for our current study. Our second contribution is to present an efficient procedure for solving a subclass of the max-t-norm-type optimization problems in which the max-product-type one is a special case, yet, the max-min-type one is not included. Numerical examples are provided to illustrate the procedure.