Some new properties of an outer measure on a σ – field

Ahmed, Ibrahim S.; Asaad, Samah H.; Ebrahim, Hassan H.

doi:10.1080/09720502.2021.1884386

Cited by 5 publications

(2 citation statements)

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“…Ahmed [3] and [4] in 2019 introduced some generalizations of σ-algebra. Many authors was studied σ-algebra, see [5], [6] and [7]. The notion of measure is studied in [8] and [9] as a set function 𝜓: ℋ ⟶ [0 , ∞] such that 𝜓 (⋃ E 𝑘 𝑘 ) = ∑ 𝜓 (E 𝑘 ) 𝑘 , whenever E 1 , E 2 , … form a finite or countably infinite collection of disjoint sets in ℋ .…”

Section: Introductionmentioning

confidence: 99%

On measure relatively to fuzzy σ–algebra

Ahmed

Ebrahim²

2022

J. Phys.: Conf. Ser.

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In this work we introduce and study some concepts relatively to fuzzy σ–algebra such as measure, countably additive, complete measure and extension of measure. Moreover, we present some of their basic properties and examples of them. In addition, it is shown that the linear combination of measure relatively to fuzzy σ–algebra is a measure too. Finally, the relationships between the proposed concepts have been introduced.

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Section: Introductionmentioning

confidence: 99%

On measure relatively to fuzzy σ–algebra

Ahmed

Ebrahim²

2022

J. Phys.: Conf. Ser.

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“…In 2019 Ahmed and Ebrahim [2] introduced some generalizations of -algebra and -ring. Many other authors are interested in studying -algebra andring, for example, see [3], [4] and [5]. Zadeh [6] in 1965 first introduced the concept of the fuzzy set where is a nonempty set, then a fuzzy set in is defined as a set of ordered pairs {…”

Section: Introduction and Basic Conceptsmentioning

confidence: 99%

γ– algebra of Sets and Some of its Properties

Ahmed

Ebrahim

Al-Fayadh³

2022

Iraqi Journal of Science

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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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