An Application of Pentagonal Neutrosophic Linear Programming for Stock Portfolio Optimization


  • Hamiden Abd El- Wahed Khalifa Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt
  • Muhammad Saeed Department of Mathematics, College of Science and Arts, Al- Badaya, Qassim University, Saudi Arabia
  • Atiqe Ur Rahman Department of Mathematics, University of Management and Technology, Lahore, 54000, Pakistan
  • Salwa El-Morsy Basic Science Department, Nile Higher Institute for Engineering and Technology, Mansoura, Egypt


Portfolio, Investment, Stock Portfolio Investment, Pentagonal Fuzzy Numbers, Score Function, TORA Software, Neutrosophic Pentagonal Fuzzy Return Rate


The Linear programming problems (LPP) have been widely applied to many real-world problems. In this study, a formulation of stock portfolio problem is proposed. The problem is formulated by involving neutrosophic pentagonal fuzzy numbers (NPFN) in the rate of risked return, expected return rate and portfolio risk amount. Based on score function, the problem is transformed to its corresponding crisp form. A solution algorithm is investigated to provide the
decision of the portfolio investment joined with investors in savings and securities. The main features of this study are: the investor can choose freely the risk coefficients to maximize the expected returns; also, the investors may determine their strategies under consideration of their own conditions. The optimal return rate is obtained by using TORA software. An example is introduced to indicate the efficiency and reliability of the technique.


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How to Cite

El- Wahed Khalifa, H. A. ., Saeed, M. ., Rahman, A. U. ., & El-Morsy, S. . . (2022). An Application of Pentagonal Neutrosophic Linear Programming for Stock Portfolio Optimization. Neutrosophic Sets and Systems, 51, 653-665. Retrieved from

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