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...

Three definitions of fuzzy random variables (FRVs) have been cited in the current literature: the first is due to Kwakernaak (1978), who viewed a FRV as a vague perception of a crisp but unobservable RV; the second is due to Puri and Ralescu (1986), who regarded FRVs as random fuzzy sets; and the third is due to Liu and Liu (2003), whose notion of FRV was based on a concept they called a credib...

There are random experiments in which the notion of a classical random variable, as a map sending each elementary event to a real number, does not capture their nature. This leads to fuzzy random variables in the Bugajski-Gudder sense. The idea is to admit variables sending the set Ω of elementary events not into the real numbers, but into the set M 1 (R) of all probability measures on the real...

The fuzzy rough sets and generalized fuzzy rough sets have been extended by three pairs of fuzzy logical operators to deal with real-valued data for a variety of models. Three pairs of fuzzy logical operators are triangular norm or t-norm and its dual (t-conorm), residual implicator or R-implicator and its dual, fuzzy implicator and t-norm, which are frequently discussed in generalization model...

This paper proposes a new method for solving a multi-objective linear programming model with fuzzy random variables. In this model, a multi-objective linear programming problem with real variables and fuzzy random coefficients is introduced. Then, a new algorithm is developed to solve the model based on the concepts of mean value of fuzzy random variables, chance-constrained programming and pie...

We obtain an improvement of strong laws of large numbers for independent fuzzy random variables.

in this paper, a model of an optimal control problem with chance constraints is introduced. the parametersof the constraints are fuzzy, random or fuzzy random variables. todefuzzify the constraints, we consider possibility levels.  bychance-constrained programming the chance constraints are converted to crisp constraints which are neither fuzzy nor stochastic and then the resulting classical op...

In this paper, a fuzzy finite element method (FFEM) for determining the responses of structures is proposed by using transformation between and random variables. Firstly, formulae establishing normal variables equivalent to symmetric triangular numbers are presented based on combination principle insufficient reason that maximum specificity. As result, analysis transferred into stochastic analy...