A Comparative study Between R-modules and Fuzzy R-modules

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Published: Oct 7, 2025
DOI: https://doi.org/10.51984/sucp.v4i3.4181
Keywords:
Modules, Fuzzy modules, Fuzzy sub modules, Fuzzy modules homomorphisms, Fuzzy quotient modules

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Magida Mohamed Ali Alsowid
Mathematics Department, Faculty of Sciences, University of Sebha
Almbrok Hussin Alsonosi Omar
Mathematics Department, Faculty of Sciences, University of Sebha

Abstract

A comparative study on the concepts and structures of classical modules in crisp set theory and fuzzy modules is presented in this article. We discuss modules, fuzzy modules, fuzzy submodules, fuzzy module homomorphisms, and fuzzy quotient modules. The paper focuses on differences in definitions and basic properties of crisp and fuzzy modules. We show that the extension from classic to fuzzy modules is a natural one and that many module-theoretic notions in the classical case can be naturally extended to hold in the fuzzy case; this may be viewed as an indication that the class of fuzzy modules generalizes that of classical modules. This extension underscores the flexibility of module theory in fuzzy environments, accommodating uncertainty and imprecision at least.

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How to Cite
Alsowid , M. M. A., & Almbrok Hussin Alsonosi Omar. (2025). A Comparative study Between R-modules and Fuzzy R-modules. Sebha University Conference Proceedings, 4(3), 56–60. https://doi.org/10.51984/sucp.v4i3.4181
Conference Proceedings Volume
Sebha University Conference Proceedings, Vol 4, No. 3, 2025: Proceeding of the 8th International Conferences of Scientific and Technology (ICST)
Section
Confrence Proceeding
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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

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