Journal
FUZZY SETS AND SYSTEMS
Volume 158, Issue 7, Pages 769-782Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.fss.2006.10.026
Keywords
fuzzy numbers; interval-valued expectation; possibilistic mean value; downside risk functions; fuzzy mathematical programming
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This paper presents two fuzzy portfolio selection models where the objective is to minimize the downside risk constrained by a given expected return. We assume that the rates of returns on securities are approximated as LR-fuzzy numbers of the same shape, and that the expected return and risk are evaluated by interval-valued means. We establish the relationship between those mean-interval definitions for a given fuzzy portfolio by using suitable ordering relations. Finally, we formulate the portfolio selection problem as a linear program when the returns on the assets are of trapezoidal form. (C) 2006 Elsevier B.V. All rights reserved.
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