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The lambda selections of parametric interval-valued fuzzy variables and their numerical characteristics

Author

Listed:
  • Ying Liu

    (Hebei University)

  • Yan-Kui Liu

    (Hebei University)

Abstract

To model the uncertainty in the secondary possibility distributions, this paper develops a new method for handling interval-valued fuzzy variables with variable lower and upper possibility distributions. For a parametric interval-valued fuzzy variable, we define its lower selection variable, upper selection variable and lambda selection variable. The three selection variables are characterized by variable possibility distributions, and their numerical characteristics like expected values and n-th moments are important indices in practical optimization and decision-making problems. Under this consideration, we establish some useful analytical expressions of the expected values and n-th moments for the lambda selections of parametric interval-valued trapezoidal, normal and Erlang fuzzy variables. Furthermore, we focus on the arithmetic about the sums of common parametric interval-valued fuzzy variables. Finally, we apply the proposed optimization indices to a quantitative finance problem, where the second moment is used to measure the risk of a portfolio.

Suggested Citation

  • Ying Liu & Yan-Kui Liu, 2016. "The lambda selections of parametric interval-valued fuzzy variables and their numerical characteristics," Fuzzy Optimization and Decision Making, Springer, vol. 15(3), pages 255-279, September.
    • Handle: RePEc:spr:fuzodm:v:15:y:2016:i:3:d:10.1007_s10700-015-9227-3
    DOI: 10.1007/s10700-015-9227-3
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    References listed on IDEAS

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    1. Chen, Ting-Yu & Chang, Chien-Hung & Rachel Lu, Jui-fen, 2013. "The extended QUALIFLEX method for multiple criteria decision analysis based on interval type-2 fuzzy sets and applications to medical decision making," European Journal of Operational Research, Elsevier, vol. 226(3), pages 615-625.
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