Affiliations: [a] School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala, Punjab, India
| [b] Department of Mathematics, College of Science and Arts, Qassim Univesity, ArRass, Saudi Arabia
| [c] Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University Giza, Egypt
| [d] Department of Mathematics, College of Science and Arts, Qassim University, Al-Badayaa, Saudi Arabia
Correspondence:
[*]
Corresponding author. Harish Garg, School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala – 147004, Punjab, India. Tel.: +91 86990 31147; E-mail: [email protected].
Abstract: Rough set theory, introduced by Pawlak in 1981, is one of the important theories to express the vagueness not by means of membership but employing a boundary region of a set, i.e., an object is approximately determined based on some knowledge. In our real-life, there exists several parameters which impact simultaneously on each other and hence dealing with such different parameters and their conflictness create a multi-objective nonlinear programming problem (MONLPP). The objective of the paper is to deal with a MONLPP with rough parameters in the constraint set. The considered MONLPP with rough parameters are converted into the two-single objective problems namely, lower and upper approximate problems by using the weighted averaging and the ɛ- constraints methods and hence discussed their efficient solutions. The Karush-Kuhn-Tucker’s optimality conditions are applied to solve these two lower and upper approximate problems. In addition, the rough weights and the rough parameter ɛ are determined by the lower and upper the approximations corresponding each efficient solution. Finally, two numerical examples are considered to demonstrate the stated approach and discuss their advantages over the existing ones.
