A note to the sum of fuzzy variables
type: Item
instance of: scholarly article
title: A note to the sum of fuzzy variables
zbMATH Open document ID: 0919.04007
DOI: 10.1016/S0165-0114(96)00233-3
author: Dug Hun Hong
author: Kim Hoyong
published in: Fuzzy Sets and Systems
publication date: 1999-08-17T00:00:00Z
review text: The paper deals with a model of fuzzy variables which is a possibilistic analogue of probability spaces and random variables. The structure composed of a set, the class of its subsets and a possibility measure, is called a pattern space; a fuzzy variable is a real-valued function on it. The sum of fuzzy variables is defined by means of the extension principle using their membership functions which are analogous to probability distributions. The attention is focused on the property of unrelativeness which is analogous to probabilistic independence. The main results show necessary and sufficient conditions under which a convex combination of unrelated fuzzy variables with identical membership function has also this membership function.
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 1283800
zbMATH Keywords: fuzzy variables
zbMATH Keywords: possibility measure
zbMATH Keywords: pattern space
zbMATH Keywords: membership functions
zbMATH Keywords: unrelativeness
reviewed by: Milan Mareš
MaRDI profile type: Publication
cites work: The law of large numbers for fuzzy processes and the estimation problem
cites work: Fuzzy sets and systems. Theory and applications
cites work: Fuzzy variables
cites work: Some comments on fuzzy variables
full work available at URL: s0165-0114(96)00233-3
OpenAlex ID: W2074906712
description: scientific article; zbMATH DE number 1283800