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On Multi-Fuzzy Rough Sets, Relations, and Topology

On Multi-Fuzzy Rough Sets, Relations, and Topology

Gayathri Varma, Sunil Jacob John
Copyright: © 2019 |Volume: 8 |Issue: 1 |Pages: 19
ISSN: 2156-177X|EISSN: 2156-1761|EISBN13: 9781522567684|DOI: 10.4018/IJFSA.2019010106
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MLA

Varma, Gayathri, and Sunil Jacob John. "On Multi-Fuzzy Rough Sets, Relations, and Topology." IJFSA vol.8, no.1 2019: pp.101-119. http://doi.org/10.4018/IJFSA.2019010106

APA

Varma, G. & John, S. J. (2019). On Multi-Fuzzy Rough Sets, Relations, and Topology. International Journal of Fuzzy System Applications (IJFSA), 8(1), 101-119. http://doi.org/10.4018/IJFSA.2019010106

Chicago

Varma, Gayathri, and Sunil Jacob John. "On Multi-Fuzzy Rough Sets, Relations, and Topology," International Journal of Fuzzy System Applications (IJFSA) 8, no.1: 101-119. http://doi.org/10.4018/IJFSA.2019010106

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Abstract

This article describes how rough set theory has an innate topological structure characterized by the partitions. The approximation operators in rough set theory can be viewed as the topological operators namely interior and closure operators. Thus, topology plays a role in the theory of rough sets. This article makes an effort towards considering closed sets a primitive concept in defining multi-fuzzy topological spaces. It discusses the characterization of multi-fuzzy topology using closed multi-fuzzy sets. A set of axioms is proposed that characterizes the closure and interior of multi-fuzzy sets. It is proved that the set of all lower approximation of multi-fuzzy sets under a reflexive and transitive multi-fuzzy relation forms a multi-fuzzy topology.

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