The Convergence of Optimal Values and Optimal Solutions of Approximation of Fuzzy Mixed Integre Programming

Since fuzzy programming with recourse problems includes fuzzy variable parameters defined through a possibility distribution, it is inherently infinite-dimensional optimization problems that can rarely be solved directly. Therefore, algorithms to solve such optimization problems must rely on intelligent computing as well as approximating scheme, which result in approximating finite-dimensional optimization problems. The purpose of this paper is to establish conditions under which the optimal objective value (resp., optimal solution) of such approximating finite-dimensional optimization problem converges to the optimal objective value (resp., optimal solution) of the true infinite-dimensional optimization problem.