Extension of the concept of mappings using fuzzy sets
type: Item
instance of: scholarly article
title: Extension of the concept of mappings using fuzzy sets
zbMATH Open document ID: 0797.04008
DOI: 10.1016/0165-0114(93)90187-M
author: Kiyomitsu Horiuchi
author: Haruo Murakami
published in: Fuzzy Sets and Systems
publication date: 1994-10-17T00:00:00Z
review text: The paper gives a new method to extend the extension principle. It is well known that the classical extension principle means that the set- value mapping \(f: 2^ X\to 2^ Y\), \(A\mapsto f(A)= \{f(x): x\in A\}\), is induced by a mapping \(f: X\to Y\). It is interesting that the authors of this paper have found the following fact: for any \(y\in f(A)\), there may be a point \(x\in X= A\) such that \(f(x)= y\), which gives us a new point of view. By doing so, the authors introduce a generalized extension principle -- the \(\mu\)-extension principle, which includes the classical extension principle as well as Zadeh's extension as special cases. For different \(\mu\) there are different extensions. So it has many applications, especially in decision making under fuzzy environment. And the authors give a comparison of the different extensions. Based on this extension, I think that there will be a lot of work to do.
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 91B06
zbMATH DE Number: 496162
zbMATH Keywords: generalized extension principle
zbMATH Keywords: decision making
zbMATH Keywords: fuzzy environment
reviewed by: Hongxing Li
MaRDI profile type: Publication
cites work: Mode-type operators on fuzzy sets
cites work: Q3309450
cites work: Fuzzy sets
description: scientific article; zbMATH DE number 496162