Exact sequences of fuzzy linear maps
type: Item
instance of: scholarly article
title: Exact sequences of fuzzy linear maps
zbMATH Open document ID: 0661.46059
DOI: 10.1016/0165-0114(88)90057-7
author: Fu-Zheng Pan
published in: Fuzzy Sets and Systems
publication date: 1988-01-01T00:00:00Z
review text: The paper deals with ``fuzzy'' versions of standard homological facts from the theory of modules (vector spaces); namely: the first isomorphism theorem for short exact sequences for fuzzy linear maps (f.l.m.) over fuzzy vector spaces the third isomorphism theorem and the 5-lemma for quasi-monic epic f.l.m, the stability property for an infinite complex of f.l.m., the property of split exactness of a short sequence and so on. Necessary concepts for these versions are introduced by the author in terms of the ``underlying'' ordinary linear map and the usual map \(\chi\) :V\(\to [0,1]\) for a fuzzy vector space \(\chi_ V.\) The key concept is the following: f.l.m. \(\tilde f:\)\(\chi_ V\to \eta_ W\) is said to be quasi-monic if \(\chi_{\ker}\tilde f=\chi_{V^*}\), where \(V^*=\{v\in V| \chi (v)=1\}\) and ker \(\tilde f:=\{v\in V| \eta (f(v))=1\}.\) Just the concept admits the technique of diagram search. Also, the author intends to set up the functor theory of fuzzy vector spaces (modules) in the near future.
Mathematics Subject Classification ID: 46M20
Mathematics Subject Classification ID: 46A99
zbMATH DE Number: 4080187
zbMATH Keywords: fuzzy versions of standard homological facts from the theory of modules
zbMATH Keywords: first isomorphism theorem for short exact sequences for fuzzy linear maps
zbMATH Keywords: fuzzy vector spaces
zbMATH Keywords: third isomorphism theorem
zbMATH Keywords: 5-lemma for quasi- monic epic
zbMATH Keywords: stability property
zbMATH Keywords: split exactness of a short sequence
MaRDI profile type: Publication
full work available at URL: 0165-0114(88)90057-7
OpenAlex ID: W2048851517
cites work: Fuzzy vector spaces and fuzzy topological vector spaces
cites work: Q4091811
cites work: Q3882615
cites work: Q3882586
cites work: Convex fuzzy sets
cites work: Fuzzy finitely generated modules
description: scientific article; zbMATH DE number 4080187