Foldness of Bipolar Fuzzy Sets and Its Application in BCK/BCI-Algebras
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,...
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| Format: | Article |
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MDPI AG
2019-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/11/1036 |
| _version_ | 1828761144107466752 |
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| author | Young Bae Jun Seok-Zun Song |
| author_facet | Young Bae Jun Seok-Zun Song |
| author_sort | Young Bae Jun |
| collection | DOAJ |
| description | 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) <i>k</i>-fold bipolar fuzzy sets is introduced, and its application in BCK/BCI-algebras is discussed. The concepts of <i>k</i>-fold bipolar fuzzy subalgebra and <i>k</i>-fold bipolar fuzzy ideal are introduced, and related properties are investigated. Characterizations of <i>k</i>-fold bipolar fuzzy subalgebra/ideal are considered, and relations between <i>k</i>-fold bipolar fuzzy subalgebra and <i>k</i>-fold bipolar fuzzy ideal are displayed. Extension of <i>k</i>-fold bipolar fuzzy subalgebra is discussed. |
| first_indexed | 2024-12-11T01:25:10Z |
| format | Article |
| id | doaj.art-dda16b5b9979482ba645da9d91e6b7fc |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-11T01:25:10Z |
| publishDate | 2019-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-dda16b5b9979482ba645da9d91e6b7fc2022-12-22T01:25:35ZengMDPI AGMathematics2227-73902019-11-01711103610.3390/math7111036math7111036Foldness of Bipolar Fuzzy Sets and Its Application in BCK/BCI-AlgebrasYoung Bae Jun0Seok-Zun Song1Department of Mathematics Education, Gyeongsang National University, Jinju 52828, KoreaDepartment of Mathematics, Jeju National University, Jeju 63243, KoreaRecent 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) <i>k</i>-fold bipolar fuzzy sets is introduced, and its application in BCK/BCI-algebras is discussed. The concepts of <i>k</i>-fold bipolar fuzzy subalgebra and <i>k</i>-fold bipolar fuzzy ideal are introduced, and related properties are investigated. Characterizations of <i>k</i>-fold bipolar fuzzy subalgebra/ideal are considered, and relations between <i>k</i>-fold bipolar fuzzy subalgebra and <i>k</i>-fold bipolar fuzzy ideal are displayed. Extension of <i>k</i>-fold bipolar fuzzy subalgebra is discussed.https://www.mdpi.com/2227-7390/7/11/1036<i>k</i>-fold bipolar fuzzy set<i>k</i>-fold bipolar fuzzy subalgebra<i>k</i>-fold bipolar fuzzy ideal |
| spellingShingle | Young Bae Jun Seok-Zun Song Foldness of Bipolar Fuzzy Sets and Its Application in BCK/BCI-Algebras Mathematics <i>k</i>-fold bipolar fuzzy set <i>k</i>-fold bipolar fuzzy subalgebra <i>k</i>-fold bipolar fuzzy ideal |
| title | Foldness of Bipolar Fuzzy Sets and Its Application in BCK/BCI-Algebras |
| title_full | Foldness of Bipolar Fuzzy Sets and Its Application in BCK/BCI-Algebras |
| title_fullStr | Foldness of Bipolar Fuzzy Sets and Its Application in BCK/BCI-Algebras |
| title_full_unstemmed | Foldness of Bipolar Fuzzy Sets and Its Application in BCK/BCI-Algebras |
| title_short | Foldness of Bipolar Fuzzy Sets and Its Application in BCK/BCI-Algebras |
| title_sort | foldness of bipolar fuzzy sets and its application in bck bci algebras |
| topic | <i>k</i>-fold bipolar fuzzy set <i>k</i>-fold bipolar fuzzy subalgebra <i>k</i>-fold bipolar fuzzy ideal |
| url | https://www.mdpi.com/2227-7390/7/11/1036 |
| work_keys_str_mv | AT youngbaejun foldnessofbipolarfuzzysetsanditsapplicationinbckbcialgebras AT seokzunsong foldnessofbipolarfuzzysetsanditsapplicationinbckbcialgebras |