Optimization in an interval-valued fuzzy environment

A new concept of the optimization problem under uncertainty is proposed and treated in the paper. It is an extension of fuzzy optimization in which the degrees of satisfaction of objective(s) and of constraints are described as an interval-value. This approach is an application of the interval-valued fuzzy (IVF) set concept to optimization problems. An approach to solving such problems is proposed and illustrated with a simple numerical example. It converts the introduced interval-valued fuzzy optimization (IVFO) problem into the crisp (non-fuzzy) one. The advantage of the IVFO problems is twofold: they give the richest apparatus for formulation of optimization problems and the solution of IVFO problems can satisfy the objective(s) with bigger degree than the analogous fuzzy optimization problem and the crisp one.