Towards neutrosophic Circumstances goal programming approach for solving multi-objective linear fractional programming problems

Alhanouf Alburaikan¹, S. A. Edalatpanah², Rabab Alharbi³, Hamiden Abd El-Wahed Khalifa^{1, 4,*}

¹ Department of Mathematics, College of Science and Arts, Qassim University, Al- Badaya, 51951, Saudi Arabia

²Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran,

⁴Department of Mathematics, College of Science and Arts, Qassim University, Ar Rass51452, Saudi Arabia

Emails:  a.albrikan@qu.edu.sa; Saedalatpanah@gmail.com; ras.Alharbi@qu.edu.sa; hamiden@cu.edu.eg

Abstract

Indeterminacy is common in practical decision-making circumstances. So the mathematical models of decision making represent the situations in a better way if the parameters are considered as neutrosophic.  This article studies a general framework of multi-objective neutrosophic linear fractional programming problem (MONLFPP) and proposes unique approach. The issue's parameters are thought of as triangular neutrosophic numbers. The problem is converted into an equal crisp multi-objective linear programming problem (MOLPP) with the help of variable transformation technique and a ranking function.  Fuzzy goal programming is used to solve the MOLPP that has been obtained. Finally, the usefulness of the proposed technique is established using two mathematical models.

Keywords: Optimization; Neutrosophic set; Triangular neutrosophic number; Score function; multi-objective linear fractional programming problem; fuzzy goal programming; Decision making