Study of Fuzzy σ-Ring  and Some Related Concepts

Main Article Content

Ibrahim S Ahmed
hassan H. Ebrahim
Ali Al-Fayadh

Abstract

This paper introduces the concept of fuzzy σ-ring as a generalization of fuzzy σ-algebra and basic properties; examples of this concept have been given.  As the first result, it has been proved that every  σ-algebra over a fuzzy set x*  is a  fuzzy σ-ring-over a fuzzy set x*  and construct their converse by example. Furthermore, the fuzzy ring  concept has been studied to generalize fuzzy algebra and its relation. Investigating  that the concept of fuzzy  σ-Ring is a stronger form of a fuzzy ring  that is every fuzzy σ-Ring over a fuzzy set x* is a fuzzy ring over a fuzzy set x* and construct their converse by example. In addition, the idea of the smallest, as an important property in the study of real analysis, is studied as well. Finally, the main goal of this paper is to study these concepts and give basic properties, examples, characterizations and relationships between them.

Article Details

How to Cite
Ahmed, I. S., Ebrahim, hassan H., & Al-Fayadh, A. (2022). Study of Fuzzy σ-Ring  and Some Related Concepts. Ibn AL- Haitham Journal For Pure and Applied Sciences, 35(2), 37–46. https://doi.org/10.30526/35.2.2767
Section
mathematics

References

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