On imaginable T-fuzzy subalgebras and imaginable T-fuzzy closed ideals in BCH-algebras
We inquire further into the properties on fuzzy closed ideals. We give a characterization of a fuzzy closed ideal using its level set, and establish some conditions for a fuzzy set to be a fuzzy closed ideal. We describe the fuzzy closed ideal generated by a fuzzy set, and give a characterization of...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201006408 |
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| _version_ | 1832561968476585984 |
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| author | Young Bae Jun Sung Min Hong |
| author_facet | Young Bae Jun Sung Min Hong |
| author_sort | Young Bae Jun |
| collection | DOAJ |
| description | We inquire further into the properties on fuzzy closed ideals. We
give a characterization of a fuzzy closed ideal using its level set, and establish some conditions for a fuzzy set to be a fuzzy closed ideal. We describe the fuzzy closed ideal generated by a
fuzzy set, and give a characterization of a finite-valued fuzzy closed ideal. Using a t-norm T, we introduce the notion of (imaginable) T-fuzzy subalgebras and (imaginable) T-fuzzy closed ideals, and obtain some related results. We give relations
between an imaginable T-fuzzy subalgebra and an imaginable
T-fuzzy closed ideal. We discuss the direct product and
T-product of T-fuzzy subalgebras. We show that the family of
T-fuzzy closed ideals is a completely distributive lattice. |
| format | Article |
| id | doaj-art-3e43578fdc2c4fffa9658077d5cd7b5f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3e43578fdc2c4fffa9658077d5cd7b5f2025-02-03T01:23:43ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0127526928710.1155/S0161171201006408On imaginable T-fuzzy subalgebras and imaginable T-fuzzy closed ideals in BCH-algebrasYoung Bae Jun0Sung Min Hong1Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, KoreaDepartment of Mathematics, Gyeongsang National University, Chinju 660-701, KoreaWe inquire further into the properties on fuzzy closed ideals. We give a characterization of a fuzzy closed ideal using its level set, and establish some conditions for a fuzzy set to be a fuzzy closed ideal. We describe the fuzzy closed ideal generated by a fuzzy set, and give a characterization of a finite-valued fuzzy closed ideal. Using a t-norm T, we introduce the notion of (imaginable) T-fuzzy subalgebras and (imaginable) T-fuzzy closed ideals, and obtain some related results. We give relations between an imaginable T-fuzzy subalgebra and an imaginable T-fuzzy closed ideal. We discuss the direct product and T-product of T-fuzzy subalgebras. We show that the family of T-fuzzy closed ideals is a completely distributive lattice.http://dx.doi.org/10.1155/S0161171201006408 |
| spellingShingle | Young Bae Jun Sung Min Hong On imaginable T-fuzzy subalgebras and imaginable T-fuzzy closed ideals in BCH-algebras International Journal of Mathematics and Mathematical Sciences |
| title | On imaginable T-fuzzy subalgebras and imaginable T-fuzzy closed ideals in BCH-algebras |
| title_full | On imaginable T-fuzzy subalgebras and imaginable T-fuzzy closed ideals in BCH-algebras |
| title_fullStr | On imaginable T-fuzzy subalgebras and imaginable T-fuzzy closed ideals in BCH-algebras |
| title_full_unstemmed | On imaginable T-fuzzy subalgebras and imaginable T-fuzzy closed ideals in BCH-algebras |
| title_short | On imaginable T-fuzzy subalgebras and imaginable T-fuzzy closed ideals in BCH-algebras |
| title_sort | on imaginable t fuzzy subalgebras and imaginable t fuzzy closed ideals in bch algebras |
| url | http://dx.doi.org/10.1155/S0161171201006408 |
| work_keys_str_mv | AT youngbaejun onimaginabletfuzzysubalgebrasandimaginabletfuzzyclosedidealsinbchalgebras AT sungminhong onimaginabletfuzzysubalgebrasandimaginabletfuzzyclosedidealsinbchalgebras |