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γ– algebra of Sets and Some of its Properties

Authors

  • Ibrahim S. Ahmed Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, Iraq https://orcid.org/0000-0003-4466-3263
  • Hassan H. Ebrahim Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, Iraq https://orcid.org/0000-0001-6931-9392
  • Ali Al-Fayadh Department of Mathematics and Computer Applications, College of Science, Al – Nahrain University, Baghdad, Iraq https://orcid.org/0000-0003-1652-9673

DOI:

https://doi.org/10.24996/ijs.2022.63.11.28

Keywords:

σ–algebra, algebra, measure, fuzzy set, outer measure

Abstract

    The main objective of this work is to generalize the concept of  fuzzy algebra by introducing the notion of  fuzzy algebra. Characterization and examples of the proposed generalization are presented, as well as several different properties of  fuzzy algebra are proven. Furthermore, the relationship between fuzzy algebra and fuzzy algebra is studied, where it is shown that the fuzzy algebra is a generalization of fuzzy algebra too. In addition, the notion of restriction, as an important property in the study of measure theory, is studied as well. Many properties of restriction of a nonempty family of fuzzy subsets of fuzzy power set are investigated and it is shown that the restriction of fuzzy algebra is fuzzy algebra too.

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Section

Mathematics

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