Generalized Direct Product of Complex Intuitionistic Fuzzy Subrings
The objective of this article is to present the notion of direct product of two complex intuitionistic fuzzy subrings. We show that the direct product of two complex intuitionistic fuzzy subrings is also complex intuitionistic fuzzy subring and discuss its various algebraic aspects. We also define t...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer
2021-01-01
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| Series: | International Journal of Computational Intelligence Systems |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/125951144/view |
| _version_ | 1828748206578597888 |
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| author | Muhammad Gulzar M. Haris Mateen Yu-Ming Chu Dilshad Alghazzawi Ghazanfar Abbas |
| author_facet | Muhammad Gulzar M. Haris Mateen Yu-Ming Chu Dilshad Alghazzawi Ghazanfar Abbas |
| author_sort | Muhammad Gulzar |
| collection | DOAJ |
| description | The objective of this article is to present the notion of direct product of two complex intuitionistic fuzzy subrings. We show that the direct product of two complex intuitionistic fuzzy subrings is also complex intuitionistic fuzzy subring and discuss its various algebraic aspects. We also define the level subsets of the direct product of two complex intuitionistic fuzzy subsets and prove that the level subset of the direct product of two complex intuitionistic fuzzy subring is subring and prove some fundamental result of this phenomena. We show that the homomorphic image (preimage) of the direct product of complex intuitionistic fuzzy subrings is a complex intuitionistic fuzzy subring by using the notion of classical homomorphism. |
| first_indexed | 2024-04-14T04:56:57Z |
| format | Article |
| id | doaj.art-5387935b74a74d168e6e053ae231c26d |
| institution | Directory Open Access Journal |
| issn | 1875-6883 |
| language | English |
| last_indexed | 2024-04-14T04:56:57Z |
| publishDate | 2021-01-01 |
| publisher | Springer |
| record_format | Article |
| series | International Journal of Computational Intelligence Systems |
| spelling | doaj.art-5387935b74a74d168e6e053ae231c26d2022-12-22T02:11:07ZengSpringerInternational Journal of Computational Intelligence Systems1875-68832021-01-0114110.2991/ijcis.d.210106.001Generalized Direct Product of Complex Intuitionistic Fuzzy SubringsMuhammad GulzarM. Haris MateenYu-Ming ChuDilshad AlghazzawiGhazanfar AbbasThe objective of this article is to present the notion of direct product of two complex intuitionistic fuzzy subrings. We show that the direct product of two complex intuitionistic fuzzy subrings is also complex intuitionistic fuzzy subring and discuss its various algebraic aspects. We also define the level subsets of the direct product of two complex intuitionistic fuzzy subsets and prove that the level subset of the direct product of two complex intuitionistic fuzzy subring is subring and prove some fundamental result of this phenomena. We show that the homomorphic image (preimage) of the direct product of complex intuitionistic fuzzy subrings is a complex intuitionistic fuzzy subring by using the notion of classical homomorphism.https://www.atlantis-press.com/article/125951144/viewComplex intuitionistic fuzzy setsComplex intuitionistic fuzzy subringsProduct of complex intuitionistic fuzzy subsetsProduct of complex intuitionistic fuzzy subringsLevel subsets of complex intuitionistic fuzzy subset |
| spellingShingle | Muhammad Gulzar M. Haris Mateen Yu-Ming Chu Dilshad Alghazzawi Ghazanfar Abbas Generalized Direct Product of Complex Intuitionistic Fuzzy Subrings International Journal of Computational Intelligence Systems Complex intuitionistic fuzzy sets Complex intuitionistic fuzzy subrings Product of complex intuitionistic fuzzy subsets Product of complex intuitionistic fuzzy subrings Level subsets of complex intuitionistic fuzzy subset |
| title | Generalized Direct Product of Complex Intuitionistic Fuzzy Subrings |
| title_full | Generalized Direct Product of Complex Intuitionistic Fuzzy Subrings |
| title_fullStr | Generalized Direct Product of Complex Intuitionistic Fuzzy Subrings |
| title_full_unstemmed | Generalized Direct Product of Complex Intuitionistic Fuzzy Subrings |
| title_short | Generalized Direct Product of Complex Intuitionistic Fuzzy Subrings |
| title_sort | generalized direct product of complex intuitionistic fuzzy subrings |
| topic | Complex intuitionistic fuzzy sets Complex intuitionistic fuzzy subrings Product of complex intuitionistic fuzzy subsets Product of complex intuitionistic fuzzy subrings Level subsets of complex intuitionistic fuzzy subset |
| url | https://www.atlantis-press.com/article/125951144/view |
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