FUZZY LINEAR PROGRAMMING WITH GRADES OF SATISFACTION IN CONSTRAINTS

Abstract

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