Soft Computing

, Volume 22, Issue 2, pp 373–385 | Cite as

Fuzzy topologies generated by fuzzy relations

Foundations
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Abstract

In this paper, we have introduced and studied fuzzy topologies generated by fuzzy relations. Several related results have been proved. In particular, we have obtained characterizations of a fuzzy topology generated by a fuzzy relation, a fuzzy topology generated by a fuzzy interval order, a preorderable fuzzy topology and an orderable fuzzy topology. We have also introduced and studied fuzzy bitopological spaces generated by fuzzy relations.

Keywords

Fuzzy relations Fuzzy topological spaces Fuzzy bitopological spaces Preorderable fuzzy topology Orderable fuzzy topology 

Notes

Acknowledgements

The S. Mishra gratefully acknowledges the financial support in the form of scholarship, given by Council of Scientific and Industrial Research, New Delhi (Award No. 09/013(0544)/2014-EMR-I), and Indian Institute of Technology (Banaras Hindu University).

Compliance with ethical standards

Conflict of interest

The R. Srivastava has no conflict of interest.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Mathematical SciencesIndian Institute of Technology (Banaras Hindu University)VaranasiIndia

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