Solving a system of infinitely many fuzzy inequalities with piecewise linear membership functions

A cutting plane type algorithm for solving a system of infinitely many fuzzy inequalities with piecewise linear membership functions is proposed. In each iteration, we solve a finite nonlinear optimization problem and add one or two more constraints. The iterative process ends when an optimal solution is identified. A convergence proof, under some mild conditions, is given. An efficient implementation based on the concepts of constraint surrogation and maximum entropy is included. Some computational results are also reported.