Some new results concerning random sets and fuzzy sets

This paper shows direct connections between fuzzy set theory and classical probability theory through the use of random sets through characterizations of random intervals one-point-coverage equivalent to fuzzy sets and the solution of the one- and multiple-point coverage problems for random sets in finite spaces.

Abstract

Abstract This paper is a continuation of past work 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.