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On neutrosophic topology

On neutrosophic topology Purpose – Recently, Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) and other kinds of sets to neutrosophic sets (NSs). Also, this author defined the notion of neutrosophic topology on the non‐standard interval. One can expect some relation between the intuitionistic fuzzy topology (IFT) on an IFS and the neutrosophic topology. This paper aims to show that this is false. Design/methodology/approach – The possible relation between the IFT and the neutrosophic topology is studied. Findings – Relations on neutrosophic topology and IFT are found. Research limitations/implications – Clearly, this paper is confined to IFSs and NSs. Practical implications – The main applications are in the mathematical field. Originality/value – The paper shows original results on fuzzy sets and topology. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Kybernetes Emerald Publishing

On neutrosophic topology

Kybernetes , Volume 37 (6): 4 – Jun 17, 2008

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Publisher
Emerald Publishing
Copyright
Copyright © 2008 Emerald Group Publishing Limited. All rights reserved.
ISSN
0368-492X
DOI
10.1108/03684920810876990
Publisher site
See Article on Publisher Site

Abstract

Purpose – Recently, Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) and other kinds of sets to neutrosophic sets (NSs). Also, this author defined the notion of neutrosophic topology on the non‐standard interval. One can expect some relation between the intuitionistic fuzzy topology (IFT) on an IFS and the neutrosophic topology. This paper aims to show that this is false. Design/methodology/approach – The possible relation between the IFT and the neutrosophic topology is studied. Findings – Relations on neutrosophic topology and IFT are found. Research limitations/implications – Clearly, this paper is confined to IFSs and NSs. Practical implications – The main applications are in the mathematical field. Originality/value – The paper shows original results on fuzzy sets and topology.

Journal

KybernetesEmerald Publishing

Published: Jun 17, 2008

Keywords: Cybernetics; Set theory; Topology

References