Study of Fuzzy σ-Ring  and Some Related Concepts

Ibrahim S Ahmed; hassan H. Ebrahim; Ali Al-Fayadh

doi:10.30526/35.2.2767

Authors

Ibrahim S Ahmed Mathematical Department /College of Computer Science and Mathematics /Tikrit University
hassan H. Ebrahim Mathematical Department /College of Computer Science and Mathematics /Tikrit University
Ali Al-Fayadh Department of Mathematics and Computer Applications / College of Science / Al – Nahrain

DOI:

https://doi.org/10.30526/35.2.2767

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.

References

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