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, has the significance to provide flexibility for the decision maker (DM), allowing for the assignment of distinct weight corresponding to each constraint and the objective function. A DM’s desired solution is produced by solving a crisp problem controlled by a parameter. We establish the validity of the proposed model and show the effect of the control parameter over the solution. We also show the effectiveness of the model and present three algorithms for solving the FLP problem. One algorithm computes a desired solution by solving a single crisp problem. The other two algorithms, interacting with the decision maker, each time compute a solution achieving a new satisfaction level. Finally, we work out an illustrative example showing that the solutions obtained are often more satisfactory than desired.