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

1
Department of Mathematics, Jeju National University, Jeju 63243, Korea
2
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(2), 177; https://doi.org/10.3390/math8020177
Received: 6 January 2020 / Revised: 23 January 2020 / Accepted: 24 January 2020 / Published: 2 February 2020
(This article belongs to the Special Issue Fuzziness and Mathematical Logic )
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 multipolar intuitionistic fuzzy set with finite degree k; k-polar intuitionistic fuzzy subalgebra; (closed) k-polar intuitionistic fuzzy ideal
MDPI and ACS Style

Kang, K.T.; Song, S.-Z.; Jun, Y.B. Multipolar Intuitionistic Fuzzy Set with Finite Degree and Its Application in BCK/BCI-Algebras. Mathematics 2020, 8, 177.

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