Characterization of order dominances on fuzzy variables for portfolio selection with fuzzy returns

Abstract

Peng et al (Int J Uncertain Fuzziness Knowl Based Syst 15:29–41, 2007) introduced, by means of the credibility measure, two dominance relations on fuzzy variables, namely the first- and the second-order dominances. In this paper, we characterize each of these dominance relations, and we justify that they satisfy six well-known properties of comparison methods. We propose a Game Theory approach for the determination of optimal portfolios when returns are fuzzy by introducing the set of best portfolios with respect to the first- and the second-order dominances. Based on the characterization of the first-order dominance, we numerically display some of the best portfolios of the classical set of portfolios of seven independent assets described by triangular fuzzy numbers.

Keywords:

• credibility measure
• fuzzy variable
• first-order dominance
• second-order dominance
• set of best portfolios

Notes

1 MU: Monetary Unit

2 Characteristics of the computer used for this implementation are: Pentium (R)4, CPU (1.80 GHZ), RAM (512 MO)