On the min-max composition of fuzzy matrices
type: Item
instance of: scholarly article
title: On the min-max composition of fuzzy matrices
zbMATH Open document ID: 0860.15013
DOI: 10.1016/0165-0114(94)00332-2
author: M. Z. Ragab
author: E. G. Emam
published in: Fuzzy Sets and Systems
publication date: 1996-10-30T00:00:00Z
review text: The paper examines the min-max product \[ (A*B)_{ij} = \min_{1\leq k\leq n} \max (a_{ik}, b_{kj}), \quad i=1, \dots, m,\;j=1, \dots,p \] of matrices \(A,B\) over the semiring \(([0,1], \min, \max)\) [cf. e.g. Chapter 3 in: \textit{A. Kandel}, \textit{S. C. Lee}, Fuzzy switching and automata, Crane Russak, New York 1979; Zbl 0406.94022)]. It is proved that \(I^*(R^*R^{-1})\) is an idempotent relation (under the max-min composition, \(I\) -- identity relation). Other properties of the min-max product are a consequence of results on the fuzzy relation composition \(A\circ B\) in virtue of Proposition 3.12: Min-max and max-min products are dual in de Morgan laws and \(A^*B= (A^c \circ B^c)^c\).
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 919432
zbMATH Keywords: fuzzy matrices
zbMATH Keywords: relation composition
zbMATH Keywords: idempotent relation
zbMATH Keywords: reflexivity
zbMATH Keywords: transitivity
zbMATH Keywords: min-max product
zbMATH Keywords: semiring
zbMATH Keywords: fuzzy relation
reviewed by: Józef Drewniak
MaRDI profile type: Publication
full work available at URL: 0165-0114(94)00332-2
OpenAlex ID: W1974479861
cites work: Fuzzy sets and systems. Theory and applications
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description: scientific article; zbMATH DE number 919432