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On product of positive L-R fuzzy numbers and its application to multi-period portfolio selection problems

Author

Listed:
  • Xiang Li

    (Beijing University of Chemical Technology)

  • Hui Jiang

    (Beijing University of Chemical Technology)

  • Sini Guo

    (The University of Hong Kong)

  • Wai-ki Ching

    (The University of Hong Kong
    Hughes Hall)

  • Lean Yu

    (Beijing University of Chemical Technology)

Abstract

With the wide applications of fuzzy theory in optimization, fuzzy arithmetic attracts great attention due to its inevitability in solution process. However, the complexity of the Zadeh extension principle significantly reduces the practicability of fuzzy optimization technology. In this paper, we prove some important properties on positive L-R fuzzy numbers, and propose a new calculation method for the product of multiple positive L-R fuzzy numbers. Furthermore, a numerical integral-based simulation algorithm (NISA) is proposed to approximate the expected value, variance and skewness of the product of positive L-R fuzzy numbers. As applications, a fuzzy multi-period utility maximization model for portfolio selection problem is considered. For handling the large number of multiplications on L-R fuzzy numbers during the optimization process, a genetic algorithm integrating NISA is designed. Finally, some numerical experiments are presented to demonstrate the advantages of NISA. The results greatly enrich the fuzzy arithmetic methods and promote the practicability of fuzzy optimization technology.

Suggested Citation

  • Xiang Li & Hui Jiang & Sini Guo & Wai-ki Ching & Lean Yu, 2020. "On product of positive L-R fuzzy numbers and its application to multi-period portfolio selection problems," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 53-79, March.
    • Handle: RePEc:spr:fuzodm:v:19:y:2020:i:1:d:10.1007_s10700-019-09308-6
    DOI: 10.1007/s10700-019-09308-6
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    References listed on IDEAS

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    1. Guo, Sini & Yu, Lean & Li, Xiang & Kar, Samarjit, 2016. "Fuzzy multi-period portfolio selection with different investment horizons," European Journal of Operational Research, Elsevier, vol. 254(3), pages 1026-1035.
    2. Lean Yu & Shouyang Wang & Fenghua Wen & Kin Lai, 2012. "Genetic algorithm-based multi-criteria project portfolio selection," Annals of Operations Research, Springer, vol. 197(1), pages 71-86, August.
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    Cited by:

    1. Guo, Sini & Gu, Jia-Wen & Ching, Wai-Ki, 2021. "Adaptive online portfolio selection with transaction costs," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1074-1086.

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