Next Article in Journal
Best Approximation of the Fractional Semi-Derivative Operator by Exponential Series
Next Article in Special Issue
Numerical Methods for Solving Fuzzy Linear Systems
Previous Article in Journal
Global Dynamics of Certain Mix Monotone Difference Equation
Previous Article in Special Issue
Hyperfuzzy Ideals in BCK/BCI-Algebras
Article Menu
Issue 1 (January) cover image

Export Article

Open AccessFeature PaperArticle
Mathematics 2018, 6(1), 11;

Length-Fuzzy Subalgebras in BCK/BCI-Algebras

Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
Department of Mathematics, Jeju National University, Jeju 63243, Korea
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]


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).

Share & Cite This Article

MDPI and ACS Style

Jun, Y.B.; Song, S.-Z.; Kim, S.J. Length-Fuzzy Subalgebras in BCK/BCI-Algebras. Mathematics 2018, 6, 11.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top