Multipolar Intuitionistic Fuzzy Set with Finite Degree and Its Application in BCK/BCI-Algebras

Kyung Tae Kang, Seok-Zun Song and Young Bae Jun
Additional contact information
Kyung Tae Kang: Department of Mathematics, Jeju National University, Jeju 63243, Korea
Seok-Zun Song: Department of Mathematics, Jeju National University, Jeju 63243, Korea
Young Bae Jun: Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea

Mathematics, 2020, vol. 8, issue 2, 1-16

Abstract: When events occur in everyday life, it is sometimes advantageous to approach them in two directions to find a solution for them. As a mathematical tool to handle these things, we can consider the intuitionistic fuzzy set. However, when events are complex and the key to a solution cannot be easily found, we feel the need to approach them for hours and from various directions. As mathematicians, we wish we had the mathematical tools that apply to these processes. If these mathematical tools were developed, we would be able to apply them to algebra, topology, graph theory, etc., from a close point of view, and we would be able to apply these research results to decision-making and/or coding theory, etc., from a distant point of view. In light of this view, the purpose of this study is to introduce the notion of a multipolar intuitionistic fuzzy set with finite degree (briefly, k -polar intuitionistic fuzzy set), and to apply it to algebraic structure, in particular, a BCK/BCI-algebra. The notions of a k -polar intuitionistic fuzzy subalgebra and a (closed) k -polar intuitionistic fuzzy ideal in a BCK/BCI-algebra are introduced, and related properties are investigated. Relations between a k -polar intuitionistic fuzzy subalgebra and a k -polar intuitionistic fuzzy ideal are discussed. Characterizations of a k -polar intuitionistic fuzzy subalgebra/ideal are provided, and conditions for a k -polar intuitionistic fuzzy subalgebra to be a k -polar intuitionistic fuzzy ideal are provided. In a BCI-algebra, relations between a k -polar intuitionistic fuzzy ideal and a closed k -polar intuitionistic fuzzy ideal are discussed. A characterization of a closed k -polar intuitionistic fuzzy ideal is considered, and conditions for a k -polar intuitionistic fuzzy ideal to be closed are provided.

Keywords: multipolar intuitionistic fuzzy set with finite degree k; k -polar intuitionistic fuzzy subalgebra; (closed) k -polar intuitionistic fuzzy ideal (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/2/177/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/2/177/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:2:p:177-:d:315582

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().