On fuzzy \(n\)-cell numbers and \(n\)-dimension fuzzy vectors
type: Item
instance of: scholarly article
title: On fuzzy \(n\)-cell numbers and \(n\)-dimension fuzzy vectors
zbMATH Open document ID: 1117.26021
author: Guixiang Wang
author: Youming Li
author: Chenglin Wen
published in: Fuzzy Sets and Systems
publication date: 2007-03-02T00:00:00Z
review text: The concepts of fuzzy \(n\)-cell numbers \(u\in{L(E^n)}\) and \(n\)-dimensional fuzzy vectors \((u_1,u_2,\ldots,u_n)\) \(\in(E)^n\) are introduced by two different ideas. Fuzzy \(n\)-cell numbers are a kind of special \(n\)-dimensional fuzzy numbers, whose sets of cuts are all hyperrectangles and it is introduced by the convenience to use. \(n\)-dimensional fuzzy vectors are the Cartesian products of \(n\) one-dimensional fuzzy numbers and it is natural to introduce. The authors show that fuzzy \(n\)-cell numbers and \(n\)-dimensional fuzzy vectors can be represented by each other (Theorem 3.1) and obtain the representations of joint member function \(u(x_1,x_2,\dots,x_n)\) and edge membership functions \(u_i(x_i)\) \((i=1,2,\ldots,n)\) by each other (Theorem 3.2). Then, the authors get the relations between \(L(E^n)\) and \((E)^n\) for the rules of operations, the metrics, the supremum (infimum), the derivative and \((k)\)integral (Theorems 3.3--3.6).
reviewed by: Congxin Wu
Mathematics Subject Classification ID: 26E50
Mathematics Subject Classification ID: 15A03
zbMATH DE Number: 5130385
zbMATH Keywords: fuzzy numbers
zbMATH Keywords: membership functions
MaRDI profile type: Publication
full work available at URL: j.fss.2006.09.006
OpenAlex ID: W173502604
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DOI: 10.1016/J.FSS.2006.09.006
description: scientific article; zbMATH DE number 5130385