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Symmetry 2018, 10(5), 174; https://doi.org/10.3390/sym10050174

Neutrosophic Hesitant Fuzzy Subalgebras and Filters in Pseudo-BCI Algebras

1
College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China
2
Department of Mathematics, School of Arts and Sciences, Shaanxi University of Science & Technology, Xi’an 710021, China
3
Department of Mathematics, College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, China
4
Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA
*
Author to whom correspondence should be addressed.
Received: 29 April 2018 / Revised: 13 May 2018 / Accepted: 14 May 2018 / Published: 18 May 2018
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Abstract

The notions of the neutrosophic hesitant fuzzy subalgebra and neutrosophic hesitant fuzzy filter in pseudo-BCI algebras are introduced, and some properties and equivalent conditions are investigated. The relationships between neutrosophic hesitant fuzzy subalgebras (filters) and hesitant fuzzy subalgebras (filters) is discussed. Five kinds of special sets are constructed by a neutrosophic hesitant fuzzy set, and the conditions for the two kinds of sets to be filters are given. Moreover, the conditions for two kinds of special neutrosophic hesitant fuzzy sets to be neutrosophic hesitant fuzzy filters are proved. View Full-Text
Keywords: pseudo-BCI algebra; hesitant fuzzy set; neutrosophic set; filter pseudo-BCI algebra; hesitant fuzzy set; neutrosophic set; filter
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Shao, S.; Zhang, X.; Bo, C.; Smarandache, F. Neutrosophic Hesitant Fuzzy Subalgebras and Filters in Pseudo-BCI Algebras. Symmetry 2018, 10, 174.

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