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The present value of a portfolio of assets with present values determined by trapezoidal ordered fuzzy numbers

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  • Anna Łyczkowska-Hanćkowiak
  • Krzysztof Piasecki

Abstract

We consider the obvious thesis that the present value of a portfolio is equal to the sum of the present values of its components. The main goal of this paper is the implementation of this thesis in the case when present values are determined by trapezoidal ordered fuzzy numbers. We apply the revised sum of ordered fuzzy numbers. The associativity of such a revised sum is investigated here. In addition, we show that the multiple revised sum of a finite sequence of trapezoidal ordered fuzzy numbers depends on the ordering of its summands. Without any obstacles, the results obtained can be generalized to the case of any ordered fuzzy numbers.

Suggested Citation

  • Anna Łyczkowska-Hanćkowiak & Krzysztof Piasecki, 2018. "The present value of a portfolio of assets with present values determined by trapezoidal ordered fuzzy numbers," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(2), pages 41-56.
    • Handle: RePEc:wut:journl:v:2:y:2018:p:41-56:id:1347
    DOI: 10.5277/ord180203
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    References listed on IDEAS

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    1. Krzysztof Piasecki & Anna Łyczkowska-Hanćkowiak, 2019. "Representation of Japanese Candlesticks by Oriented Fuzzy Numbers," Econometrics, MDPI, vol. 8(1), pages 1-24, December.
    2. Krzysztof Piasecki, 2012. "The basis of financial arithmetic from the viewpoint of utility theory," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 22(3), pages 37-53.
    3. Gutiérrez, Isabel, 1989. "Fuzzy numbers and net present value," Scandinavian Journal of Management, Elsevier, vol. 5(2), pages 149-159.
    4. Piasecki Krzysztof & Siwek Joanna, 2015. "Behavioural Present Value Defined as Fuzzy Number – a New Approach," Folia Oeconomica Stetinensia, Sciendo, vol. 15(2), pages 27-41, December.
    5. repec:wut:journl:v:3:y:2012:id:1044 is not listed on IDEAS
    6. Cédric Lesage, 2001. "Discounted cash-flows analysis: An interactive fuzzy arithmetic approach," Post-Print hal-00485731, HAL.
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    Citations

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    Cited by:

    1. Krzysztof Piasecki & Anna Łyczkowska-Hanćkowiak, 2019. "Representation of Japanese Candlesticks by Oriented Fuzzy Numbers," Econometrics, MDPI, vol. 8(1), pages 1-24, December.
    2. Anna Łyczkowska-Hanćkowiak & Aleksandra Wójcicka-Wójtowicz, 2023. "On portfolio analysis using oriented fuzzy numbers for the trade-related sector of the Warsaw Stock Exchange," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(4), pages 155-170.
    3. Krzysztof Piasecki & Anna Łyczkowska-Hanćkowiak, 2021. "Oriented Fuzzy Numbers vs. Fuzzy Numbers," Mathematics, MDPI, vol. 9(5), pages 1-27, March.

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