γ– algebra of Sets and Some of its Properties

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

doi:10.24996/ijs.2022.63.11.28

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.