### Abstract

The fundamental goal of portfolio optimization is to optimally allocate funds between different investment alternatives. The mean-variance (MV) methodology has become the most important quantitative tool used which considers the trade-off between risk and return. However the classical Markowitz's MV method does not match the real world in numerous circumstances, thus researchers done are to improve and modify the MV model to represent the practicality. This paper discusses on a portfolio selection model that extends the classical Markowitz's mean-variance model where the returns is represented by pentagonal fuzzy numbers. The concept of alpha level set is used to define the expected return and variance of fuzzy number. The proposed model gives better performance as compared to classical mean-variance model. Numerical examples are also presented to illustrate the usability of the model.

Original language | English |
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Title of host publication | Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017 |

Subtitle of host publication | Mathematical Sciences as the Core of Intellectual Excellence |

Publisher | American Institute of Physics Inc. |

Volume | 1974 |

ISBN (Electronic) | 9780735416819 |

DOIs | |

Publication status | Published - 28 Jun 2018 |

Event | 25th National Symposium on Mathematical Sciences: Mathematical Sciences as the Core of Intellectual Excellence, SKSM 2017 - Kuantan, Pahang, Malaysia Duration: 27 Aug 2017 → 29 Aug 2017 |

### Other

Other | 25th National Symposium on Mathematical Sciences: Mathematical Sciences as the Core of Intellectual Excellence, SKSM 2017 |
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Country | Malaysia |

City | Kuantan, Pahang |

Period | 27/8/17 → 29/8/17 |

### Fingerprint

### Keywords

- Mean-variance
- Pentagonal fuzzy
- Portfolio optimization

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017: Mathematical Sciences as the Core of Intellectual Excellence*(Vol. 1974). [020066] American Institute of Physics Inc.. https://doi.org/10.1063/1.5041597

**Optimal solution of fuzzy optimization using pentagonal fuzzy numbers.** / Ramli, Suhailywati; Jaaman @ Sharman, Saiful Hafizah.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017: Mathematical Sciences as the Core of Intellectual Excellence.*vol. 1974, 020066, American Institute of Physics Inc., 25th National Symposium on Mathematical Sciences: Mathematical Sciences as the Core of Intellectual Excellence, SKSM 2017, Kuantan, Pahang, Malaysia, 27/8/17. https://doi.org/10.1063/1.5041597

}

TY - GEN

T1 - Optimal solution of fuzzy optimization using pentagonal fuzzy numbers

AU - Ramli, Suhailywati

AU - Jaaman @ Sharman, Saiful Hafizah

PY - 2018/6/28

Y1 - 2018/6/28

N2 - The fundamental goal of portfolio optimization is to optimally allocate funds between different investment alternatives. The mean-variance (MV) methodology has become the most important quantitative tool used which considers the trade-off between risk and return. However the classical Markowitz's MV method does not match the real world in numerous circumstances, thus researchers done are to improve and modify the MV model to represent the practicality. This paper discusses on a portfolio selection model that extends the classical Markowitz's mean-variance model where the returns is represented by pentagonal fuzzy numbers. The concept of alpha level set is used to define the expected return and variance of fuzzy number. The proposed model gives better performance as compared to classical mean-variance model. Numerical examples are also presented to illustrate the usability of the model.

AB - The fundamental goal of portfolio optimization is to optimally allocate funds between different investment alternatives. The mean-variance (MV) methodology has become the most important quantitative tool used which considers the trade-off between risk and return. However the classical Markowitz's MV method does not match the real world in numerous circumstances, thus researchers done are to improve and modify the MV model to represent the practicality. This paper discusses on a portfolio selection model that extends the classical Markowitz's mean-variance model where the returns is represented by pentagonal fuzzy numbers. The concept of alpha level set is used to define the expected return and variance of fuzzy number. The proposed model gives better performance as compared to classical mean-variance model. Numerical examples are also presented to illustrate the usability of the model.

KW - Mean-variance

KW - Pentagonal fuzzy

KW - Portfolio optimization

UR - http://www.scopus.com/inward/record.url?scp=85049806511&partnerID=8YFLogxK

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U2 - 10.1063/1.5041597

DO - 10.1063/1.5041597

M3 - Conference contribution

AN - SCOPUS:85049806511

VL - 1974

BT - Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017

PB - American Institute of Physics Inc.

ER -