دراسة مقارنة بين الوحدات النمطية والوحدات الضبابية

المؤلفون

  • ماجدة محمد علي السويدي قسم الرياضيات،كلية العلوم،جامعة سبها
  • المبروك حسين السنوسي عمر قسم الرياضيات،كلية العلوم،جامعة سبها

DOI:

https://doi.org/10.51984/sucp.v4i3.4181

الكلمات المفتاحية:

الموديلات ، والموديلات الضبابية، والموديلات الفرعية الضبابية، وتشاكلات الموديلات الضبابية، وموديلات حاصل القسمة الضبابية.

الملخص

تقدم هذه المقالة دراسة مقارنة بين الوحدات الكلاسيكية في نظرية المجموعات الدقيقة والوحدات الضبابية، وذلك بفحص مفاهيمها الأساسية وخصائصها الهيكلية. تشمل الجوانب الرئيسية التي تم تحليلها الوحدات، والوحدات الضبابية، والوحدات الضبابية الفرعية، وتشاكلات الوحدات الضبابية، ووحدات حاصل القسمة الضبابية. تُركز الدراسة على الاختلافات في التعريفات والخصائص الأساسية بين الوحدات الدقيقة وضبابية. تُظهر النتائج أن العديد من مفاهيم نظرية الوحدات الكلاسيكية يمكن توسيعها بشكل طبيعي لتشمل الوحدات الضبابية، مما يشير إلى أن الوحدات الضبابية تُعمم الوحدات الكلاسيكية. يُؤكد هذا التوسيع على مرونة نظرية الوحدات في البيئات الضبابية، مُراعيةً عدم اليقين وعدم الدقة.

المراجع

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Wisbauer, R. (2018). Foundations of module and ring theory. Routledge.‏

Zadeh,L. A. (1965). Fuzzy sets, information and control. Information and control, 8(3), 338-353.‏

Rosenfeld, A. (1971). Fuzzy groups. Journal of mathematical analysis and applications, 35(3), 512-517.‏

Negoita, C. V., Ralescu, D. A., & Gottwald, S. (1977). Applications of fuzzy sets to systems analysis. IEEE Transactions on Systems, Man, and Cybernetics, 7(9), 679-680.‏

Nanda, S. (1985). Fuzzy Modules over fuzzy rings (No. IC--85/237). International Centre for Theoretical Physics, Trieste (Italy).

Pan, F. Z. (1988). Fuzzy quotient modules. Fuzzy sets and Systems, 28(1), 85-90.‏

Tercan, A., & Yücel, C. C. (2016). Module theory. Extending Modules and Generalizations, Bassel: Birkhäuser–Springer.‏

Sidky, F. I. (2001). On radicals of fuzzy submodules and primary fuzzy submodules. Fuzzy sets and systems, 119(3), 419-425.‏

Yetkin, E., & Olgun, N. (2014). A new type fuzzy module over fuzzy rings. The Scientific World Journal, 2014(1), 730932.

Hamel, M. A., & Khalaf, H. Y. (2020). fuzzy Maximal Sub-modules. Iraqi Journal of science, 1164-1172.‏

Chemat, B., & Chinram, R. (2022). Properties of Uniform Fuzzy Modules and Semiuniform Fuzzy Modules. Journal of the Indonesian Mathematical Society, 133-146.‏

Priestley, H. A. (2011). Introduction to Groups, Rings and Fields. HT andTT,https://people.maths.ox.ac. uk/flynn/genus2/sheets0405/grfnotes1011. pdf.‏

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Auslander, M., & Buchsbaum, D. (2014). Groups, rings, modules. Courier Corporation.‏

Bhattacharya, N. P., & Bhattacharya, P. (1986). Fuzzy groups: some group-theoretic analogs. Information Sciences, 39(3), 247-267.‏

Goldman, M. A. (2004). Ring theory.‏

التنزيلات

منشور


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2025-10-07

كيفية الاقتباس

دراسة مقارنة بين الوحدات النمطية والوحدات الضبابية. (2025). وقائع مؤتمرات جامعة سبها, 4(3), 56-60. https://doi.org/10.51984/sucp.v4i3.4181

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