Solving Fully Fuzzy Linear Programming Problems using The Fuzzy Chaos Approach

In this paper, an application of fuzzy chaos to a fuzzy linear programming problem with fuzzy goals, fuzzy constraints, and fuzzy variables is proposed. The application of the fuzzy chaos approach to a fuzzy linear programming problem is demonstrated in a concrete case. The model is illustrated with a numerical example of the maximization of the profit of a manufacturing company. The optimal solution to the investigated problem is discussed. The performed investigations show that centroids of the fuzzy numbers, satisfying the constraints can exceed the optimal crisp values and, consequently, the optimal value of the crisp objective function. On the other hand, the fuzzy representation of the objective function also contributes to the centroid of the optimal value of the objective function which can slightly exceed the optimal crisp value. It should be noted that when optimizing certain real processes, the representation of both the constraints and the objective function might be fuzzy. Therefore, it is purposive to solve the problem using the fuzzy approach without its conversion to the crisp linear programming problem, which is more effective. The discussion of the numerical example results shows that it is purposeful to solve the optimization problem using the fuzzy approach without its conversion to the crisp linear programming problem, which is more effective.