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Journals / Journal of Engineering Technology and Applied Sciences / 2023 / Cilt: 8 Sayı: 3

On 1-Absorbing Fuzzy Ideals of Commutative Semirings

Doç. Dr. Erdoğan Mehmet Özkan(YILDIZ TECHNICAL UNIVERSITY)0000-0003-2341-6626
Serkan Onar(YILDIZ TECHNICAL UNIVERSITY)0000-0003-3084-7694
Ayten Ozkan(YILDIZ TECHNICAL UNIVERSITY)0000-0002-3948-1943
İlayda Kaplan(YILDIZ TECHNICAL UNIVERSITY)0000-0002-6198-1573
Pages
131–141
Publication Date
2023-12-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Furthermore, these theorems are elucidated through specific examples.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, the algebraic structure of 1-absorbing ideals is first examined and applied to fuzzy sets, along with an investigation into the relationships and algebraic properties between them.
📊
Key Findings & Data:The contribution to this work's literature involves examining 1-absorbing fuzzy primary ideals.
💡
Conclusion & Impact:Furthermore, these theorems are elucidated through specific examples.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Fuzzy sets · Fuzzy ideals · 1-absorbing ideals

Abstract

In this study, the algebraic structure of 1-absorbing ideals is first examined and applied to fuzzy sets, along with an investigation into the relationships and algebraic properties between them. The contribution to this work's literature involves examining 1-absorbing fuzzy primary ideals. Features of 1-absorbing fuzzy primary ideals are explored, and it is demonstrated, for instance, that I is deemed a 1-absorbing fuzzy primary ideal of P if I is a fuzzy primary ideal of P. Additionally, I is considered a 2-absorbing fuzzy primary ideal of P if I is a 1-absorbing fuzzy primary ideal of P. Furthermore, these theorems are elucidated through specific examples.

🔖

Cite This Article

Özkan, D. D. E. M., Onar, S., Ozkan, A., Kaplan, İ. (2023). On 1-Absorbing Fuzzy Ideals of Commutative Semirings. Journal of Engineering Technology and Applied Sciences, Cilt: 8 Sayı: 3, 131–141. https://doi.org/10.30931/jetas.1302897

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  35. Roberts, D. W., “Ordination based on fuzzy set theory”, Vegetation 66(3) (1986): 123-131.
  36. Zimmermann, H. J., “Fuzzy set theory”, Wiley interdisciplinary reviews: Computational statistics 2(3) (2010): 317-332.
  37. Chang, C. L., “Fuzzy topological spaces”, Journal of Mathematical Analysis and Applications 24(1) (1968): 182-190.
  38. Rosenfeld, A., “Fuzzy groups”, Journal of Mathematical Analysis and applications 35(3) (1971): 512-517.
  39. Liu, W. J., “Fuzzy invariant subgroups and fuzzy ideals”, Fuzzy sets and Systems 8(2) (1982): 133-139.
  40. Abou-Zaid, S., “On fuzzy subnear-rings and ideals”, Fuzzy sets and systems 44(1) (1991): 139-146.
  41. Atanassov, K. T., “Intuitionistic fuzzy sets. In Intuitionistic fuzzy sets”, Physica, Heidelberg (1999): 1-137.
  42. Szmidt, E., and Kacprzyk, J., “Distances between intuitionistic fuzzy sets”, Fuzzy sets and systems 114(3) (2000): 505-518.
  43. Özdemir, O., & Kalınkara, Y., “Bulanık Mantık: 2000-2020 Yılları Arası Tez ve Makale Çalışmalarına Yönelik Bir İçerik Analizi”, Acta Infologica 4(2) (2020): 155-174.
  44. Badawi, A., “On 2-absorbing ideals of commutative rings”, Bulletin of the Australian Mathematical Society 75(3) (2007): 417-429.
  45. Badawi, A., & Celikel, E. Y., “On 1-absorbing primary ideals of commutative rings”, Journal of Algebra and Its Applications 19(06) (2020): 2050111.
  46. Mandal, D., “On 2-absorbing fuzzy ideals of commutative semirings”, TWMS Journal of Applied and Engineering Mathematics 11(2) (2021): 368.
  47. Darani, A.Y., Hashempoor, A., “L-fuzzy 0-(1-or 2-or 3-) 2-absorbing ideals in semiring”, Ann. Fuzzy Math. Inform. 7 (2014): 303-311.
  48. Jonathan S. Golan, “Semirings and their applications”, Springer (2013): 105-120.
  49. Darani, Ahmad Yousefian, “On 2-absorbing and weakly 2-absorbing ideals of commutative semirings”, Kyungpook Mathematical Journal 52 (1) (2012): 91-97.
  50. Chaudhari, Jayprakash Ninu, “2-absorbing ideals in semirings”, International Journal of Al- gebra 6 (6) (2012): 265-270.
  51. Groenewald, Nico, “On weakly 2-absorbing ideals of non-commutative rings”, Afrika Matematika 32(7-8) (2021): 1669-1683.
  52. Behzadipour, Hussein, and Peyman Nasehpour, “On 2-absorbing ideals of commutative semir- ings”, Journal of Algebra and Its Applications 19 (2)(2020): 2050034.
  53. Jaber, Ameer., “Properties of weakly 2-absorbing primal ideals”, Italian Journal of Pure and Applied Mathematics 7 (2022): 609-619.
  54. Groenewald, N. J., “On 2-absorbing and weakly 2-absorbing principally right primary ideals”, Journal of Algebra and Related Topics 9 (2) (2021): 47-67.
  55. Sahoo, Taptee, Deepak Shetty, M., Groenewald, N. J., Harikrishnan, P. K., Kuncham, S. P., “On completely 2-absorbing ideals of N-groups”, Journal of Discrete Mathematical Sciences and Cryptography 24 (2) (2021): 541-556.
  56. Yassine, A., M. J. Nikmehr, and R. Nikandish., “On 1-absorbing prime ideals of commutative rings”, Journal of Algebra and its Applications 20(10) (2021): 2150175.
  57. Koc, Suat, Ünsal Tekir, and Eda Yıldız, “On weakly 1-absorbing prime ideals”, Ricerche di Matematica 72(2) (2023): 723-738.
  58. Groenewald, Nico., “1-absorbing prime ideals and weakly 1-absorbing prime ideals in non-commutative rings”, S˜ao Paulo Journal of Mathematical Sciences (2022): 1-17.
  59. Bouba, E. M., Tamekkante, M., Tekir, U¨., and Ko¸c, S., “Notes on 1-absorbing prime ideals”,Proceedings of the Bulgarian Academy of Sciences 75(5) (2022): 631-639.
  60. Abu-Dawwas, R., Yıldız, E., Tekir, U¨., Koc, S., “On graded 1-absorbing prime ideals.” Sao Paulo Journal of Mathematical Sciences 15 (2021): 450-462.
  61. Anbarloei, Mahdi., “On 1-absorbing prime hyperideal and some of its generalizations”, Journal of Mathematics (2022): 4947019.
  62. Saleh, Mohammad, and Ibaa M., “On weakly 1-absorbing primary ideals of commutative semirings”, Communications in Advanced Mathematical Sciences 5(4) (2022): 199-208.