Post-optimality analysis on the membership functions of a fuzzy linear programming problem*

Models of linear programming problems with fuzzy constraints are very well known in the current literature. In almost all cases, to solve these problems, linear membership functions are used because they have very good properties and are very easy to manipulate. In some cases, however, because of the knowledge that the decision maker has, such membership functions could be modeled as nonlinear, although the complexity of the problem could increase. This paper considers the use of nonlinear membership functions in fuzzy linear programming problems to show that the corresponding solution to be obtained can be derived from a parallel linear model. Moreover, it is easier to solve than the nonlinear model, making use of a similar procedure to that of post-optimal analysis in classical linear programming. The case in which these membership functions are defined by means of piecewise linear approximations is also considered and analyzed.