A Parametric Approach to Fuzzy Linear Programming

In this paper we discuss how to deal with decision problems that are described with LP models and formulated with elements of imprecision and uncertainty. More precisely, we will study LP models in which the parameters are not fully known but only with some degree of precision. Even with incomplete information the model builder (or model user) is normally able to give a realistic interval for the parameters of an LP model. For the constraint vector this is combined with some wishes or some leeway on the constraints. Even with ambiquity in the objective function, there is normally some preference ordering to be found among alternative ways of action. We will demonstrate that these modelling complications can be handled with the help of some results developed in the theory of fuzzy sets. After an overview of some central contributions to fuzzy linear programming, we will develop an LP model in which the parameters are not fully known, only with some degree of precision, and show that the model can be parametrised in such a way that the optimal solution becomes a function of the degree of precision. The fuzzy LP model derived in this way appears to be fairly easy to handle computationally, which is demonstrated with a numerical example.