Fuzzy Random Variables*

In practice we are often faced with random experiments whose outcomes are not numbers (or vectors in &I”) but are expressed in inexact linguistic terms. As an example, consider a group of individuals chosen at random who are questioned about the weather on a particular city on a particular winter day. Some possible answers would be “cold,” “more or less cold,” “very cold,” “ extremely cold,” and so on. A natural question which arises with reference to this example is: What is the average opinion about the weather in that particular city? A possible way of handling situations like this is by using the concepts of fuzzy sets and fuzzy functions [24] found useful in many applications, notably in pattern recognition, clustering, information retrieval, and systems analysis (cf. [ 161). Motivated by examples of the type given above and related problems (especially concerning group opinions), we introduce fuzzy random variables and their expectations, and we investigate some of their properties.