MEAN-SEMIVARIANCE MODELS FOR PORTFOLIO OPTIMIZATION PROBLEM WITH MIXED UNCERTAINTY OF FUZZINESS AND RANDOMNESS

In practice, security returns cannot be accurately predicted due to lack of historical data. Therefore, statistical methods and experts' experience are always integrated to estimate future security returns, which are hereinafter regarded as random fuzzy variables. Random fuzzy variable is a powerful tool to deal with the portfolio optimization problem including stochastic parameters with ambiguous expected returns. In this paper, we first define the semivariance of random fuzzy variable and prove its several properties. By considering the semivariance as a risk measure, we establish the mean-semivariance models for portfolio optimization problem with random fuzzy returns. We design a hybrid algorithm with random fuzzy simulation to solve the proposed models in general cases. Finally, we present a numerical example and compare the results to illustrate the mean-semivariance model and the effectiveness of the algorithm.

A SUFFICIENT AND NECESSARY CONDITION FOR CHANCE DISTRIBUTIONS OF RANDOM FUZZY VARIABLES

A random fuzzy variable is a function from a credibility space to the set of random variables. Chance distribution is a type of mathematical description of random fuzzy variables. This paper presents a sufficient and necessary condition for chance distributions of random fuzzy variables.

Expected Value Operator of Random Fuzzy Variable and Random Fuzzy Expected Value Models

Random fuzzy variable is mapping from a possibility space to a collection of random variables. This paper first presents a new definition of the expected value operator of a random fuzzy variable, and proves the linearity of the operator. Then, a random fuzzy simulation approach, which combines fuzzy simulation and random simulation, is designed to estimate the expected value of a random fuzzy variable. Based on the new expected value operator, three types of random fuzzy expected value models are presented to model decision systems where fuzziness and randomness appear simultaneously. In addition, random fuzzy simulation, neural networks and genetic algorithm are integrated to produce a hybrid intelligent algorithm for solving those random fuzzy expected valued models. Finally, three numerical examples are provided to illustrate the feasibility and the effectiveness of the proposed algorithm.