In this paper, we consider portfolio selection problem in which security returns are regarded as fuzzy variables rather than random variables. We first introduce a concept of absolute deviation for fuzzy variables and prove some useful properties, which imply that absolute deviation may be used to measure risk well. Then we propose two mean-absolute deviation models by defining risk as abs...

This thesis develops the idea of probabilistic arithmetic The aim is to replace arithmetic operations on numbers with arithmetic operations on random variables Speci cally we are interested in numerical methods of calculating convolutions of probability distributions The long term goal is to be able to handle random prob lems such as the determination of the distribution of the roots of random ...

In this paper, weak laws of large numbers for sum of independent and identically distributed fuzzy random variables are obtained.

Clouds are a concept for uncertainty mediating between the concept of a fuzzy set and that of a probability distribution. A cloud is to a random variable more or less what an interval is to a number. We discuss the basic theoretical and numerical properties of clouds, and relate them to histograms, cumulative distribution functions, and likelihood ratios. We show how to compute nonlinear transf...

This paper discusses multiproduct aggregate production planning (APP) decision making problems in fuzzy random environments. To maximize the chance of obtaining the profit more than the predetermined profit over the whole planning horizon, a fuzzy random APP model is established, in which the market demand, production cost, subcontracting cost, inventory carrying cost, backorder cost, product c...

In this paper a fuzzy method for determining appropriate structural design is presented. Non-stochastic uncertainty is quantified using fuzzy values and fuzzy random variables. Fuzzy structural parameters are processed on the basis of a generally applicable numerical method for arbitrary nonlinear fuzzy structural analyses. Fuzzy randomness is introduced into a fuzzy probabilistic safety assess...

This paper considers a general 0-1 random fuzzy programming problem including some previous 0-1 stochastic and fuzzy programming problems. The proposal problem is not a well-defined problem due to including random fuzzy variables. Therefore, by introducing chance constraint and fuzzy goal for objective function and considering the maximization for the degrees of possibility that the objective f...

This paper considers a general 0-1 random fuzzy programming problem based on the degree of necessity including some previous 0-1 stochastic and fuzzy programming problems. The proposal problem is not a well-defined problem due to including random fuzzy variables. Therefore, by introducing chance constraint and fuzzy goal for objective function, and considering the maximization for the degrees o...