Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution
Hamiden Abd El- Wahed Khalifa1,2, Faisal Al-Sharqi3,*, Ashraf Al-Quran4, Zahari Rodzi5, Heba Ghareb Goma6, Abdalwali Lutfi 7,8,9
1Department of Mathematics, College of Science and Arts, Qassim University, Al- Badaya 51951, Saudi Arabia.
2Department of Operations and Management Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt.
3Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq
4 Preparatory Year Deanship, King Faisal University, Hofuf, Al-Ahsa, 31982, Saudi Arabia
5College of Computing, Informatics and Mathematics, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 73000 Negeri Sembilan, Malaysia
6 Department of Mathematics and Statistics, Institute for Management Information Systems, Suiz, Egypt, E-Mail:
7Department of Accounting, College of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia
8MEU Research Unit, Middle East University, Amman, Jordan
9Applied Science Research Center, Applied Science Private University, Amman 11931, Jordan
Emails: Ha.Ahmed@qu.edu.sa; hamiden@cu.edu.eg; faisal.ghazi@uoanbar.edu.iq aalquran@kfu.edu.sa; zahari@uitm.edu.my; dr.heba@suezmis.edu.eg; aalkhassawneh@kfu.edu.sa
Abstract
In this paper, a bi-level chance constrained programming problem is considered when the coefficients of the objective function is presented as neutrosophic numbers and the right- hand side of the constraints is normal variables and the constraints have a joint probability distribution. While the probability problem and applying the score and accurate functions the problem is converted into an equivalent deterministic non- linear programming problem, a fuzzy programming approach is applied by defining membership function. A linear membership function is used for obtaining optimal compromise solution. A numerical example is given to illustrate the proposed methodology.
Keywords: Optimization; neutrosophic set; single valued neutrosophic numbers Chance- constrained programming; Bi- level linear programming; Decision Making; Normal distribution; Joint constraints; Incomplete Gamma function; Membership function; Fuzzy programming approach; Optimal compromise solution