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

Xiang Li, Hui Jiang, Sini Guo (), Wai-ki Ching and Lean Yu ()
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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

Fuzzy Optimization and Decision Making, 2020, vol. 19, issue 1, No 4, 53-79

Abstract: 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.

Keywords: Fuzzy sets; Fuzzy arithmetic; Positive L-R fuzzy number; Multi-period portfolio selection (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10700-019-09308-6

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