A Class of Multiple Objective Mathematical Programming Problems in a Rough Environment

This paper presents a set of multiple objective programming problems in a rough environment. These problems are classified into five 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 completely and efficient (Pareto optimal) solutions of rough multiple objective programming problems. In order to obtain these solutions we need certain theorems which we derive. Finally, we illustrate our results by examples.