Document Type : Research Paper

Authors

1 Department of Mathematics, Ganesh Dutt College, Begusarai, India.

2 Department of Mathematics, Lalit Narayan Mithila University, Darbhanga, India.

Abstract

Stock portfolio problems are one of the most relevant real-world problems. In this study, we discuss the portfolio's risk amount, rate of risk-return, and expected return rate under a Fermatean fuzzy environment. A linear programming problem is used to formulate a Fermatean fuzzy portfolio. The Fermatean fuzzy portfolio is converted to a deterministic form using the score function. Lingo software is used to solve these deterministic portfolio problems. The main feature of this model is that investors can select a risk coefficient to enhance predicted returns and customize their strategies according to their circumstances. An example is offered that illustrates the effectiveness and dependability of the proposed approach.

Keywords

Main Subjects

[1]     Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353.
[2]     Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy sets and systems, 20(1), 87–96. DOI:10.1016/S0165-0114(86)80034-3
[3]     Yager, R. R. (2014). Pythagorean membership grades in multicriteria decision making. IEEE transactions on fuzzy systems, 22(4), 958–965. DOI:10.1109/TFUZZ.2013.2278989
[4]     Senapati, T., & Yager, R. R. (2020). Fermatean fuzzy sets. Journal of ambient intelligence and humanized computing, 11(2), 663–674. DOI:10.1007/s12652-019-01377-0
[5]     Abbasi Shureshjani, R., & Shakouri, B. (2021). A comment on “A novel parametric ranking method for intuitionistic fuzzy numbers.” Big data and computing visions, 1(3), 156–160.
[6]     Zeb, A., Khan, A., Fayaz, M., & Izhar, M. (2022). Aggregation operators of Pythagorean fuzzy bi-polar soft sets with application in multiple attribute decision making. Granular computing, 7(4), 931–950. DOI:10.1007/s41066-021-00307-w
[7]     Sahoo, L. (2021). A new score function based Fermatean fuzzy transportation problem. Results in control and optimization, 4, 100040. https://doi.org/10.1016/j.rico.2021.100040
[8]     Jing, D., Imeni, M., Edalatpanah, S. A., Alburaikan, A., & Khalifa, H. A. E. W. (2023). Optimal selection of stock portfolios using multi-criteria decision-making methods. Mathematics, 11(2), 415. DOI:10.3390/math11020415
[9]     Goldfarb, D., & Iyengar, G. (2003). Robust portfolio selection problems. Mathematics of operations research, 28(1), 1–38. DOI:10.1287/moor.28.1.1.14260
[10]   Khalifa, H. A. E. W., & Kumar, P. (2020). Solving fully neutrosophic linear programming problem with application to stock portfolio selection. Croatian operational research review, 11(2), 165–176. DOI:10.17535/CRORR.2020.0014
[11]   Liu, Y., & Qin, Z. (2012). Mean semi-absolute deviation model for uncertain portfolio optimization problem. Journal of uncertain systems, 6(4), 299–307.
[12]   Markowitz, H. M. (1952). Portfolio selection. the journal of finance, 7(1), 71–91.
[13]   Simamora, I., & Sashanti, R. (2016). Optimization of fuzzy portfolio considering stock returns and downside risk. International journal of science and research (IJSR), 5(4), 141–145. DOI:10.21275/v5i4.nov162491
[14]   Rasoulzadeh, M., Edalatpanah, S. A., Fallah, M., & Najafi, S. E. (2022). A multi-objective approach based on markowitz and dea cross-efficiency models for the intuitionistic fuzzy portfolio selection problem. Decision making: applications in management and engineering, 5(2), 241–259. DOI:10.31181/dmame0324062022e
[15]   Saberhoseini, S. F., Edalatpanah, S. A., & Sorourkhah, A. (2022). Choosing the best private-sector partner according to the risk factors in neutrosophic environment. Big data and computing visions, 2(2), 61–68. DOI:10.22105/bdcv.2022.334005.1075
[16]   Sardou, I. G., Nazari, A., Ghodsi, E., & Bagherzadeh, E. (2015). Optimal portfolio selection using multi-objective fuzzy-genetic method. International journal, 3(2), 99–103.
[17]   Wu, H., & Li, Z. (2011). Multi-period mean-variance portfolio selection with Markov regime switching and uncertain time-horizon. Journal of systems science and complexity, 24(1), 140–155. DOI:10.1007/s11424-011-9184-z
[18]   Yin, D. (2018). Application of interval valued fuzzy linear programming for stock portfolio optimization. Applied mathematics, 09(02), 101–113. DOI:10.4236/am.2018.92007
[19]   Yager, R. R. (2013). Pythagorean fuzzy subsets. Proceedings of the 2013 joint IFSA world congress and NAFIPS annual meeting, IFSA/NAFIPS 2013 (pp. 57–61). IEEE. DOI: 10.1109/IFSA-NAFIPS.2013.6608375