Two new operators on fuzzy matrices.
type: Item
instance of: scholarly article
title: Two new operators on fuzzy matrices.
zbMATH Open document ID: 1058.15023
DOI: 10.1007/BF02935748
author: Amiya K. Shyamal
author: Madhumangal Pal
published in: Journal of Applied Mathematics and Computing
publication date: 2004-09-28T00:00:00Z
review text: Matrices over lattices were firstly considered by \textit{M. Yoeli} [Am Math. Monthly 68, 552--557 (1961; Zbl 0115.02103)] and \textit{T. S. Blyth} [J. Lond. Math. Soc. 39, 427--432 (1964; Zbl 0154.01104)]. \textit{M. G. Thomason} [J. Math. Anal. Appl. 57, 476--480 (1977; Zbl 0345.15007)] considered the particular case: matrices over the lattice \(([0,1],\max,\min)\) and called them `fuzzy matrices'. This paper deals with such matrices as matrices of fuzzy relations on a finite set (relation notions are used for matrices). The title `new operators' were introduced by \textit{L. A. Zadeh} [Inf. Control 8, 338--353 (1965; Zbl 0139.24606)] as algebraic union and intersection of fuzzy sets and fuzzy relations, and examined in details by \textit{L. T. Kóczy} and \textit{M. Hajnal} [Probl. Control Inform. Theory 6, 47--66 (1977; Zbl 0358.02017)]. Now, the authors prove (Properties 2 and 6), that fuzzy relation properties as symmetry, reflexivity and irreflexivity are preserved by the decribed union and intersection of fuzzy relations (cf. also \textit{V. Peneva} and \textit{I. Popchev} [Fuzzy Sets Syst. 139, 615--633 (2003; Zbl 1054.91021)]).
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 08A72
Mathematics Subject Classification ID: 68T37
zbMATH DE Number: 2103973
zbMATH Keywords: fuzzy set
zbMATH Keywords: fuzzy relation
zbMATH Keywords: matrix of fuzzy relation
zbMATH Keywords: fuzzy matrix
zbMATH Keywords: reflexive relation
zbMATH Keywords: symmetric relation
zbMATH Keywords: matrices over lattices
reviewed by: Józef Drewniak
MaRDI profile type: Publication
cites work: Canonical form of a transitive fuzzy matrix
cites work: Iterates of fuzzy circulant matrices
cites work: Q3432255
cites work: Generalized fuzzy matrices
cites work: Canonical form of a strongly transitive fuzzy matrix
cites work: Determinant theory for fuzzy matrices
cites work: The determinant and adjoint of a square fuzzy matrix
cites work: On the min-max composition of fuzzy matrices
cites work: Pattern Classification Based on Fuzzy Relations
cites work: Convergence of powers of a fuzzy matrix
cites work: Q4224429
cites work: Controllable fuzzy matrices
cites work: Convergence of powers of controllable fuzzy matrices
description: scientific article; zbMATH DE number 2103973