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

Abstract

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 e cient (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.

Fuzzy Rough Programming Models: An Expected Value Perspective

“…In order to simplify a model's establishment in an expert system or a knowledge-based system, Chung et al [9] put forward a new fuzzy multiple choice goal programming model to resolve a kind of linear MOP problem, and verified its effectiveness in reducing computational complexity during the solutions and practicability in providing satisfactory solutions. Hamzehee et al [10] introduced a set of MOP problems under the rough environments and further categorized them into five types depending on the location of roughness in the decision set or the objectives. In the above models, the uncertainties, i.e., roughness, randomness and fuzziness, are treated as several single parts.…”

Achievement Stability Set for Parametric Rough Linear Goal Programing Problem

“…In RST, any vague concept is replaced by a pair of precise concepts called the lower and the upper approximations of the vague concept. For a vague concept X, a lower approximation is contained in all objects which surely belong to the concept X and an upper approximation contains all objects which possibly belong to the concept X [22].…”

“…In recent decades, RST has been used as the fundamental tool in many applications including optimization problems [22,23]. For the mathematical programing problems in the crisp environment, the aim is to maximize (minimize) an objective function over a certain set of feasible solutions.…”

“…One of the ways by which DM can specify them by using RST. The RST has a significant role in the following applications artificial intelligence, machine learning, and decision analysis, knowledge discovery from databases, expert systems, and pattern recognition [22].…”

“…The duality of multi-objective rough convex programing problems was setup by Elsisy et al [28]. A class of multi-objective mathematical programing problems in a rough environment has been developed by Hamzehee et al [22]. Elsisy et al presented a qualitative analysis of parametric rough convex programing when parameters in the objective function and roughness in the constraints [29].…”