Fuzzy linear programming with grades of satisfaction in constraints

We present a new model and a new approach for solving fuzzy linear programming (FLP) problems with various utilities for the satisfaction of the fuzzy constraints. The model, constructed as a multi-objective linear programming problem, provides flexibility for the decision maker (DM), and allows for the assignment of distinct weights to the constraints and the objective function. The desired solution is obtained by solving a crisp problem controlled by a parameter. We establish the validity of the proposed model and study the effect of the control parameter on the solution. We also illustrate the efficiency of the model and present three algorithms for solving the FLP problem, the first of which obtains a desired solution by solving a single crisp problem. The other two algorithms, interact with the decision maker, and compute a solution which achieves a given satisfaction level. Finally, we present an illustrative example showing that the solutions obtained are often even more satisfactory than asked for.