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Mathematics 2018, 6(1), 11; https://doi.org/10.3390/math6010011

Length-Fuzzy Subalgebras in BCK/BCI-Algebras

1
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
2
Department of Mathematics, Jeju National University, Jeju 63243, Korea
3
Department of Mathematics, Natural Science of College, Gyeongsang National University, Jinju 52828, Korea
*
Author to whom correspondence should be addressed.
Received: 1 December 2017 / Revised: 3 January 2018 / Accepted: 5 January 2018 / Published: 12 January 2018
(This article belongs to the Special Issue Fuzzy Mathematics)
Full-Text   |   PDF [248 KB, uploaded 12 January 2018]

Abstract

As a generalization of interval-valued fuzzy sets and fuzzy sets, the concept of hyperfuzzy sets was introduced by Ghosh and Samanta in the paper [J. Ghosh and T.K. Samanta, Hyperfuzzy sets and hyperfuzzy group, Int. J. Advanced Sci Tech. 41 (2012), 27–37]. The aim of this manuscript is to introduce the length-fuzzy set and apply it to B C K / B C I -algebras. The notion of length-fuzzy subalgebras in B C K / B C I -algebras is introduced, and related properties are investigated. Characterizations of a length-fuzzy subalgebra are discussed. Relations between length-fuzzy subalgebras and hyperfuzzy subalgebras are established. View Full-Text
Keywords: hyperfuzzy set; hyperfuzzy subalgebra; length of hyperfuzzy set; length-fuzzy subalgebra hyperfuzzy set; hyperfuzzy subalgebra; length of hyperfuzzy set; length-fuzzy subalgebra
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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Jun, Y.B.; Song, S.-Z.; Kim, S.J. Length-Fuzzy Subalgebras in BCK/BCI-Algebras. Mathematics 2018, 6, 11.

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