Fuzzy linear programming duality

The word "duality" has been used in various areas of science for long time. Nevertheless, in general, there is a lack of consensus about the exact meaning of this important notion. However, in the field of optimization, and particularly in linear programming, the notion of duality is well understood and remarkably useful. Various attempts to develop analogous useful duality schemes for linear programming involving fuzzy data have been appearing since the early days of fuzzy sets. After recalling basic results on linear programming duality, we give examples of early attempts in extending duality to problems involving fuzzy data, and then we discuss recent results on duality in fuzzy linear programming and their possible application.