Bipolar Fuzzy UP-Algebras
In this paper, we apply the notion of bipolar-valued fuzzy set to UP-algebras. We introduce the notions of bipolar fuzzy UP-subalgebras (resp., bipolar fuzzy UP-filters, bipolar fuzzy UP-ideals, and bipolar fuzzy strongly UP-ideals) of UP-algebras and prove their generalizations. We provide a condit...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-11-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/23/4/69 |
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| author | Korawut Kawila Chaiphon Udomsetchai Aiyared Iampan |
| author_facet | Korawut Kawila Chaiphon Udomsetchai Aiyared Iampan |
| author_sort | Korawut Kawila |
| collection | DOAJ |
| description | In this paper, we apply the notion of bipolar-valued fuzzy set to UP-algebras. We introduce the notions of bipolar fuzzy UP-subalgebras (resp., bipolar fuzzy UP-filters, bipolar fuzzy UP-ideals, and bipolar fuzzy strongly UP-ideals) of UP-algebras and prove their generalizations. We provide a condition for a bipolar fuzzy UP-filter to be a bipolar fuzzy UP-ideal. Further, we discuss the relation between bipolar fuzzy UP-subalgebras (resp., bipolar fuzzy UP-filters, bipolar fuzzy UP-ideals, and bipolar fuzzy strongly UP-ideals) and their level cuts. |
| first_indexed | 2024-12-12T16:22:53Z |
| format | Article |
| id | doaj.art-90078f4f758649df918f457c452503eb |
| institution | Directory Open Access Journal |
| issn | 2297-8747 |
| language | English |
| last_indexed | 2024-12-12T16:22:53Z |
| publishDate | 2018-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-90078f4f758649df918f457c452503eb2022-12-22T00:18:56ZengMDPI AGMathematical and Computational Applications2297-87472018-11-012346910.3390/mca23040069mca23040069Bipolar Fuzzy UP-AlgebrasKorawut Kawila0Chaiphon Udomsetchai1Aiyared Iampan2Department of Mathematics, School of Science, University of Phayao, Phayao 56000, ThailandDepartment of Mathematics, School of Science, University of Phayao, Phayao 56000, ThailandDepartment of Mathematics, School of Science, University of Phayao, Phayao 56000, ThailandIn this paper, we apply the notion of bipolar-valued fuzzy set to UP-algebras. We introduce the notions of bipolar fuzzy UP-subalgebras (resp., bipolar fuzzy UP-filters, bipolar fuzzy UP-ideals, and bipolar fuzzy strongly UP-ideals) of UP-algebras and prove their generalizations. We provide a condition for a bipolar fuzzy UP-filter to be a bipolar fuzzy UP-ideal. Further, we discuss the relation between bipolar fuzzy UP-subalgebras (resp., bipolar fuzzy UP-filters, bipolar fuzzy UP-ideals, and bipolar fuzzy strongly UP-ideals) and their level cuts.https://www.mdpi.com/2297-8747/23/4/69UP-algebrabipolar fuzzy UP-subalgebrabipolar fuzzy UP-filterbipolar fuzzy UP-idealbipolar fuzzy strongly UP-ideal |
| spellingShingle | Korawut Kawila Chaiphon Udomsetchai Aiyared Iampan Bipolar Fuzzy UP-Algebras Mathematical and Computational Applications UP-algebra bipolar fuzzy UP-subalgebra bipolar fuzzy UP-filter bipolar fuzzy UP-ideal bipolar fuzzy strongly UP-ideal |
| title | Bipolar Fuzzy UP-Algebras |
| title_full | Bipolar Fuzzy UP-Algebras |
| title_fullStr | Bipolar Fuzzy UP-Algebras |
| title_full_unstemmed | Bipolar Fuzzy UP-Algebras |
| title_short | Bipolar Fuzzy UP-Algebras |
| title_sort | bipolar fuzzy up algebras |
| topic | UP-algebra bipolar fuzzy UP-subalgebra bipolar fuzzy UP-filter bipolar fuzzy UP-ideal bipolar fuzzy strongly UP-ideal |
| url | https://www.mdpi.com/2297-8747/23/4/69 |
| work_keys_str_mv | AT korawutkawila bipolarfuzzyupalgebras AT chaiphonudomsetchai bipolarfuzzyupalgebras AT aiyarediampan bipolarfuzzyupalgebras |