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Open AccessArticle

Foldness of Bipolar Fuzzy Sets and Its 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
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1036; https://doi.org/10.3390/math7111036
Received: 14 September 2019 / Revised: 24 October 2019 / Accepted: 25 October 2019 / Published: 3 November 2019
(This article belongs to the Special Issue General Algebraic Structures)
Recent trends in modern information processing have focused on polarizing information, and and bipolar fuzzy sets can be useful. Bipolar fuzzy sets are one of the important tools that can be used to distinguish between positive information and negative information. Positive information, for example, already observed or experienced, indicates what is guaranteed to be possible, and negative information indicates that it is impossible, prohibited, or certainly false. The purpose of this paper is to apply the bipolar fuzzy set to BCK/BCI-algebras. The notion of (translated) k-fold bipolar fuzzy sets is introduced, and its application in BCK/BCI-algebras is discussed. The concepts of k-fold bipolar fuzzy subalgebra and k-fold bipolar fuzzy ideal are introduced, and related properties are investigated. Characterizations of k-fold bipolar fuzzy subalgebra/ideal are considered, and relations between k-fold bipolar fuzzy subalgebra and k-fold bipolar fuzzy ideal are displayed. Extension of k-fold bipolar fuzzy subalgebra is discussed. View Full-Text
Keywords: k-fold bipolar fuzzy set; k-fold bipolar fuzzy subalgebra; k-fold bipolar fuzzy ideal k-fold bipolar fuzzy set; k-fold bipolar fuzzy subalgebra; k-fold bipolar fuzzy ideal
MDPI and ACS Style

Jun, Y.B.; Song, S.-Z. Foldness of Bipolar Fuzzy Sets and Its Application in BCK/BCI-Algebras. Mathematics 2019, 7, 1036.

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