Implementing Fuzzy Random Variables -- Some Preliminary Observations

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 credibility measure. Given the different rationales, three questions arise: (1) how is each of these views of FRVs conceptualized; (2) what are the differences and similarities between the metrics for each of these views, and (3) how are the metrics for these three views implemented. The purpose of this article is to present some preliminary observations with respect to the answers to these questions.