On Interval-valued Anti Fuzzy Prime bi-ideal of Semigroup
In this paper, we introduce the notions of interval-valued anti fuzzy prime (resp. strongly prime and semiprime) bi-ideals of semigroup. By using these ideas, we characterize those semigroup for which each interval anti-fuzzy bi-ideal is semiprime and strongly prime. • Introduction: The theory...
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| Language: | English |
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Tikrit University
2023-02-01
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| Series: | Tikrit Journal of Pure Science |
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| Online Access: | https://tjpsj.org/index.php/tjps/article/view/956 |
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| author | S. A. Wuhaib Akram S. Mohammed Zeyad. M. Abdullah |
| author_facet | S. A. Wuhaib Akram S. Mohammed Zeyad. M. Abdullah |
| author_sort | S. A. Wuhaib |
| collection | DOAJ |
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In this paper, we introduce the notions of interval-valued anti fuzzy prime (resp. strongly prime and semiprime) bi-ideals of semigroup. By using these ideas, we characterize those semigroup for which each interval anti-fuzzy bi-ideal is semiprime and strongly prime.
• Introduction: The theory of fuzzy sets proposed by Zadeh [6], in his classic paper of 1965, deal with the applications of fuzzy technology in information processing. Mordeson, Malik and Kuroki gave a systematic exposition fuzzy semigroups in [2], where one can find theoretical results on fuzzy semigroups. Shabir and Kanwal [5], introduced the concept of prime bi-ideal, strongly prime bi-ideals and semiprime bi-ideal of a semigroup and studied those semigroups.
In this paper we introduced the concept of interval valued anti fuzzy prime, strongly prime and semiprime bi-ideal of semigroups and give characterization of semigroups in terms of these notions we characterize those semigroups for which each interval-valued anti fuzzy bi-ideal is semiprime and strongly irreducible.
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| format | Article |
| id | doaj-art-26fb873ab08a4e2681591a0bb930c735 |
| institution | Kabale University |
| issn | 1813-1662 2415-1726 |
| language | English |
| publishDate | 2023-02-01 |
| publisher | Tikrit University |
| record_format | Article |
| series | Tikrit Journal of Pure Science |
| spelling | doaj-art-26fb873ab08a4e2681591a0bb930c7352025-08-20T03:50:21ZengTikrit UniversityTikrit Journal of Pure Science1813-16622415-17262023-02-0121110.25130/tjps.v21i1.956On Interval-valued Anti Fuzzy Prime bi-ideal of SemigroupS. A. WuhaibAkram S. MohammedZeyad. M. Abdullah In this paper, we introduce the notions of interval-valued anti fuzzy prime (resp. strongly prime and semiprime) bi-ideals of semigroup. By using these ideas, we characterize those semigroup for which each interval anti-fuzzy bi-ideal is semiprime and strongly prime. • Introduction: The theory of fuzzy sets proposed by Zadeh [6], in his classic paper of 1965, deal with the applications of fuzzy technology in information processing. Mordeson, Malik and Kuroki gave a systematic exposition fuzzy semigroups in [2], where one can find theoretical results on fuzzy semigroups. Shabir and Kanwal [5], introduced the concept of prime bi-ideal, strongly prime bi-ideals and semiprime bi-ideal of a semigroup and studied those semigroups. In this paper we introduced the concept of interval valued anti fuzzy prime, strongly prime and semiprime bi-ideal of semigroups and give characterization of semigroups in terms of these notions we characterize those semigroups for which each interval-valued anti fuzzy bi-ideal is semiprime and strongly irreducible. https://tjpsj.org/index.php/tjps/article/view/956On Interval-valuedbi-idealSemigroup |
| spellingShingle | S. A. Wuhaib Akram S. Mohammed Zeyad. M. Abdullah On Interval-valued Anti Fuzzy Prime bi-ideal of Semigroup Tikrit Journal of Pure Science On Interval-valued bi-ideal Semigroup |
| title | On Interval-valued Anti Fuzzy Prime bi-ideal of Semigroup |
| title_full | On Interval-valued Anti Fuzzy Prime bi-ideal of Semigroup |
| title_fullStr | On Interval-valued Anti Fuzzy Prime bi-ideal of Semigroup |
| title_full_unstemmed | On Interval-valued Anti Fuzzy Prime bi-ideal of Semigroup |
| title_short | On Interval-valued Anti Fuzzy Prime bi-ideal of Semigroup |
| title_sort | on interval valued anti fuzzy prime bi ideal of semigroup |
| topic | On Interval-valued bi-ideal Semigroup |
| url | https://tjpsj.org/index.php/tjps/article/view/956 |
| work_keys_str_mv | AT sawuhaib onintervalvaluedantifuzzyprimebiidealofsemigroup AT akramsmohammed onintervalvaluedantifuzzyprimebiidealofsemigroup AT zeyadmabdullah onintervalvaluedantifuzzyprimebiidealofsemigroup |