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Computing the Mean Chance Distributions of Fuzzy Random Variables
, 2008
"... Fuzzy random variable is a combination of fuzzy variable and random variable, and can characterize both fuzziness and randomness in the real world. The mean chance of a fuzzy random event is an important concept in fuzzy random optimization, just like the probability of a stochastic event in stochas ..."
Abstract

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Fuzzy random variable is a combination of fuzzy variable and random variable, and can characterize both fuzziness and randomness in the real world. The mean chance of a fuzzy random event is an important concept in fuzzy random optimization, just like the probability of a stochastic event in stochastic optimization and the credibility of a fuzzy event in fuzzy optimization. In fuzzy random programming, the constraints are always represented by the mean chance function of fuzzy random events, so it is difficult to solve them directly. In this paper, we deduce the formulas for the mean chance of fuzzy random events in some special cases such as the fuzzy random variables are trapezoidal fuzzy random variables for normal fuzzy random variables. The obtained formulas are very useful in fuzzy random optimization problems when we design algorithm to solve them.
Fuzzy Portfolio Selection based on ValueatRisk
"... AbstractIn this paper, using ValueatRisk, a new fuzzy portfolio selection model named VaRFPSM is proposed. The ValueatRisk is the measure of risk, which describes the greatest loss of an investment with some confidence level. When security returns are same kind of fuzzy variable, we derive tw ..."
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AbstractIn this paper, using ValueatRisk, a new fuzzy portfolio selection model named VaRFPSM is proposed. The ValueatRisk is the measure of risk, which describes the greatest loss of an investment with some confidence level. When security returns are same kind of fuzzy variable, we derive two crisp equivalent forms of the VaRFPSM. Furthermore, in general situations, we designed a fuzzy simulation based particle swarm optimization (PSO) algorithm to find an approximately optimal result. To illustrate the proposed model and hybrid PSO algorithm, a numerical example is provided and some discussions on the results are given.