Fuzzy random variables

There are two important sources of uncertainty: randomness and fuzziness. Randomness models the stochastic variability of all possible outcomes of a situation, and fuzziness relates to the unsharp boundaries of the parameters of the model. In this sense, randomness is largely an instrument of a normative analysis that focuses on the future, while fuzziness is more an instrument of a descriptive analysis reflecting the past and its implications. Clearly, randomness and fuzziness are complementary, and so a natural question is how fuzzy variables could interact with the type of random variables found in actuarial science. This article focuses on one important dimension of this issue, fuzzy random variables (FRVs). The goal is to introduce IME readers to FRVs and to illustrate how naturally compatible and complementary randomness and fuzziness are.