A class of multi-objective mathematical programming problems in a rough environment

This paper presents a set of multi-objective programming problems in a rough environment. These problems are classied into ve classes according to the location of the roughness in the objective functions or the feasible set. We study the class in which all of the objective functions are crisp and the feasible region is a rough set and, in particular, discuss the properties of the complete and ecient (Pareto optimal) solutions of rough multi-objective programming problems. In order to obtain these solutions, we need certain theorems, which we derive. Finally, we illustrate our results by examples.