Next Article in Journal / Special Issue
Fuzzy Analogues of Sets and Functions Can Be Uniquely Determined from the Corresponding Ordered Category: A Theorem
Previous Article in Journal
On Solutions to the Set-Theoretical Yang-Baxter Equation in Wajsberg-Algebras
Previous Article in Special Issue
Managing Interacting Criteria: Application to Environmental Evaluation Practices
Article Menu

Export Article

Open AccessArticle
Axioms 2018, 7(1), 7; doi:10.3390/axioms7010007

Cubic Interval-Valued Intuitionistic Fuzzy Sets and Their Application 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: 28 December 2017 / Revised: 12 January 2018 / Accepted: 15 January 2018 / Published: 23 January 2018
(This article belongs to the Special Issue New Trends in Fuzzy Set Theory and Related Items)
View Full-Text   |   Download PDF [303 KB, uploaded 23 January 2018]

Abstract

As a new extension of a cubic set, the notion of a cubic interval-valued intuitionistic fuzzy set is introduced, and its application in B C K / B C I -algebra is considered. The notions of α -internal, β -internal, α -external and β -external cubic IVIF set are introduced, and the P-union, P-intersection, R-union and R-intersection of α -internal and α -external cubic IVIF sets are discussed. The concepts of cubic IVIF subalgebra and ideal in B C K / B C I -algebra are introduced, and related properties are investigated. Relations between cubic IVIF subalgebra and cubic IVIF ideal are considered, and characterizations of cubic IVIF subalgebra and cubic IVIF ideal are discussed. View Full-Text
Keywords: α-internal; β-internal; α-external; β-external cubic interval-valued intuitionistic fuzzy set; cubic interval-valued intuitionistic fuzzy subalgebra; cubic interval-valued intuitionistic fuzzy ideal α-internal; β-internal; α-external; β-external cubic interval-valued intuitionistic fuzzy set; cubic interval-valued intuitionistic fuzzy subalgebra; cubic interval-valued intuitionistic fuzzy ideal
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).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Jun, Y.B.; Song, S.-Z.; Kim, S.J. Cubic Interval-Valued Intuitionistic Fuzzy Sets and Their Application in BCK/BCI-Algebras. Axioms 2018, 7, 7.

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

1

Comments

[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top