Enhancing neutrosophic fuzzy goal programming approach for solving multi-objective probabilistic linear programming problems
S. A. Edalatpanah 1, Hamiden Abd El- Wahed Khalifa2,3*, Ashraf Al-Quran4, Faisal Al-Sharqi5, Zahari Rodzi6, Abdalwali Lutfi7,8,9
1Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran
2Department of Mathematics, College of Science and Arts, Al- Badaya 51951, Qassim University, Saudi Arabia
3Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
4Preparatory Year Deanship, King Faisal University, Hofuf, Al-Ahsa, 31982, Saudi Arabia
5Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq
6College of Computing, Informatics and Mathematics, UiTM Cawangan Negeri Sembilan, KampusSeremban, 70300 Negeri Sembilan, Malaysia
7 Department of Accounting, College of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia
8 MEU Research Unit, Middle East University, Amman, Jordan
9Applied Science Research Center, Applied Science Private University, Amman 11931, Jordan
Emails: Saedalatpanah@gmail.com; Ha.Ahmed@qu.edu.sa; hamiden@cu.edu.eg; aalquran@kfu.edu.sa; faisal.ghazi@uoanbar.edu.iq; zahari@uitm.edu.my; aalkhassawneh@kfu.edu.sa
Abstract
This article considers a stochastic multi-objective linear programming problem in a neutrosophic framework. The right-hand sides of the constraints are random variables associated with their means and variances, and the single-valued trapezoidal neutrosophic numbers are included in the coefficients of the objective functions to investigate the problem. The problem is successfully converted into the related deterministic programming model based on the formulation of the scoring function and several distributions, such as the Uniform, Exponential, and Gama distributions. Applying fuzzy goal programming, the deterministic problem is solved. An example is then solved to demonstrate the solution methodology.
Keywords: Optimization; Optimization problems; Multi-objective stochastic linear programming; Neutrosophic numbers; Exponential distribution; Uniform distribution; Gama Distribution; Fuzzy programming; Optimal compromise solution; Optimization Problems; Decision Making; Goal programming; Lingo computer package.