Fuzzy \(G\)-equivalences and \(G\)-congruences on a groupoid under semibalanced maps
type: Item
instance of: scholarly article
title: Fuzzy \(G\)-equivalences and \(G\)-congruences on a groupoid under semibalanced maps
zbMATH Open document ID: 0937.20043
DOI: 10.1016/S0165-0114(97)00299-6
author: K. C. Gupta
author: Tajinder Pal Singh
published in: Fuzzy Sets and Systems
publication date: 2000-02-13T00:00:00Z
review text: In the present note we obtain some basic results for \(G\)-equivalences and \(G\)-congruences. For two nonempty sets \(X\) and \(Y\), we call a mapping \(f\colon X\times X\to Y\times Y\) a semibalanced map if (i) given \(a\in X\), there exists \(u\in Y\) such that \(f(a,a)=(u,u)\), and (ii) \(f(a,a)=(u,u)\), \(f(b,b)=(v,v)\) imply that \(f(a,b)=(u,v)\). We highlight the fact that the role of semibalanced maps for \(G\)-equivalences and \(G'\)-congruences is analogous to that of isomorphisms for classical algebraic structures.
Mathematics Subject Classification ID: 20N25
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 20N02
zbMATH DE Number: 1370002
zbMATH Keywords: fuzzy groups
zbMATH Keywords: fuzzy congruences
zbMATH Keywords: \(G\)-equivalences
zbMATH Keywords: \(G\)-congruences
zbMATH Keywords: semibalanced maps
MaRDI profile type: Publication
Wikidata QID: Q127412056
full work available at URL: s0165-0114(97)00299-6
OpenAlex ID: W2012466900
description: scientific article; zbMATH DE number 1370002