\(I\)-fuzzy topological groups
type: Item
instance of: scholarly article
title: \(I\)-fuzzy topological groups
zbMATH Open document ID: 1205.54003
author: Conghua Yan
author: Sheng-Zhang Guo
published in: Fuzzy Sets and Systems
publication date: 2010-07-28T00:00:00Z
review text: \textit{D. H. Foster} [J. Math. Anal. Appl. 67, 549--564 (1979; Zbl 0409.22001)] first introduced the notion of fuzzy topological groups. In the present paper, the concept of \(I\)-fuzzy topological groups is introduced and fundamental framework of \(I\)-fuzzy topological groups is established. This notion is a generalization of \(I\)-topological groups. A characterization of products of \(I\)-fuzzy topological groups in terms of \(I\)-fuzzy quasi-coincident neighbourhood systems is obtained. A characterization of \(I\)-fuzzy topological groups in terms of the corresponding \(I\)-fuzzy quasi coincidence neighbourhood systems at \(e_{\lambda}\) (\(\lambda\in [0, 1]\)) is studied. The relation between the category of \(I\)-fuzzy topological groups and the category of antichain \(I\)-topological groups is discussed. It is shown that the category of \(I\)-fuzzy topological groups and fuzzy continuous homomorphisms is isomorphic to the category of antichain \(I\)-topological groups and \(I\)-continuous homomorphisms; and the category of \(I\)-fuzzy topological groups is topological over the category of groups with respect to the forgetful functor. A direction for further study is given by the authors.
reviewed by: Bhavana Deshpande
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 22A99
zbMATH DE Number: 5762273
zbMATH Keywords: I-fuzzy topology
zbMATH Keywords: I-fuzzy quasi-coincident neighbourhood system
MaRDI profile type: Publication
full work available at URL: j.fss.2010.02.005
OpenAlex ID: W2093200173
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DOI: 10.1016/J.FSS.2010.02.005
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description: scientific article; zbMATH DE number 5762273