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

Ying Liu and Yan-Kui Liu ()
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Ying Liu: Hebei University
Yan-Kui Liu: Hebei University

Fuzzy Optimization and Decision Making, 2016, vol. 15, issue 3, No 2, 255-279

Abstract: 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.

Keywords: Interval-valued fuzzy variable; Selection variable; Variable possibility distribution; Moment; Portfolio optimization (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10700-015-9227-3

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