Some new results concerning random sets and fuzzy sets (Q801590)

This paper is a continuation of past work by the author [see e.g., Fuzzy information and decision processes, 203-211 (1982; Zbl 0519.04001)] showing direct connections between fuzzy set theory and classical probability theory through the use of random sets. This includes characterizations of random intervals one-point-coverage equivalent to fuzzy sets, determination of all nested random sets equivalent to fuzzy sets, the solution of the one- and multiple-point coverage problems for random sets in finite spaces, and the use of entropy for ordering random sets within the class of one-point-coverage-equivalent ones for any given fuzzy set. Finally, a connection between random variables, random sets, and fuzzy sets is pointed out.