Theory and applications of fuzzy random variables

We discuss the historical perspective of concepts of fuzziness and randomness, with emphasis on fuzzy random variables. We will describe the analysis of the interpretation, modeling, and impact of fuzzy random variables. Examples will be given of scenarios modeled by fuzzy random variables. Also, main approaches using fuzzy random variables will be discussed. The theoretical concept of expected value will be one of our main focus points. Finally, we present some statistical applications of fuzzy random variables mainly to statistical testing of hypotheses and to regression analysis with imprecise data.