Some new results concerning random sets and fuzzy sets
type: Item
instance of: scholarly article
title: Some new results concerning random sets and fuzzy sets
zbMATH Open document ID: 0552.60007
DOI: 10.1016/0020-0255(84)90019-7
published in: Information Sciences
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 60A99
zbMATH DE Number: 3879795
zbMATH Keywords: random sets
zbMATH Keywords: characterizations of random intervals
zbMATH Keywords: fuzzy sets
author: I. R. Goodman
MaRDI profile type: Publication
full work available at URL: 0020-0255(84)90019-7
OpenAlex ID: W2032620816
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description: scientific article; zbMATH DE number 3879795