Using fuzzy numbers in linear programming

Managers, decision makers, and experts dealing with optimization problems often have a lack of information on the exact values of some parameters used in their problems. To deal with this kind of imprecise data, fuzzy sets provide a powerful tool to model and solve these problems. This paper studies a linear programming (LP) problem in which all its elements are defined as fuzzy sets. Special cases of this general model are found and reproduced, and it is shown that they coincide with the particular problems proposed in the literature by different authors and distinct approaches. Solution methods are also provided. They show how it is possible to address and solve linear programming problems with data given in a qualitative form, instead of the usual quantitative and precise way.