Duality in fuzzy linear programming with possibility and necessity relations

A class of fuzzy linear programming (FLP) problems with fuzzy coefficients based on fuzzy relations is introduced, the concepts of feasible and (α,β)-maximal and minimal solutions are defined. The class of crisp (classical) LP problems can be embedded into the class of FLP ones. Moreover, for FLP problems a new concept of duality is introduced and the weak and strong duality theorems are derived. The introduced concepts and results are illustrated and discussed on a simple numerical example.