Heuristic algorithm for an optimal solution of fully fuzzy transportation problem

Several problems involving uncertainties can be modeled with fuzzy numbers according to the type of these uncertainties. It is natural to express the solution to such a problem with fuzzy numbers. In this study, we consider the fully fuzzy transportation problem. All input parameters of the problem are expressed with fuzzy numbers given in the parametric form. We propose a new heuristic algorithm to approximate the fuzzy optimal solution. The fuzzy problem is solved by transforming it into two independent parametric problems with the proposed method. We first divide the interval [0, 1] into a sufficiently large number of equal intervals, then write a linear programming problem for each partition point and solve these problems by transforming them into transportation problems. The proposed algorithm is supported by examples.