Decomposition Method for Solving Integer Linear Programming Problems with Trapezoidal Fuzzy Numbers

In this paper, integer linear programming with trapezoidal fuzzy numbers is studied. The trapezoidal fuzzy numbers are assumed as the coefficient of the problem and it is also assumed that decision variables are trapezoidal fuzzy variables. We prove that four crisp linear systems are needed to be solved in order to solve the trapezoidal fuzzy linear system. We also prove that solving a trapezoidal fuzzy integer linear programming problem requires solving four crisp integer linear programming problems. Based on the theorems, a decomposition method is proposed to solve the problem. A numerical example is presented to illustrate the method.