Modern classes of fuzzy $ \alpha $-covering via rough sets over two distinct finite sets

Amal T. Abushaaban; O. A. Embaby; Abdelfattah A. El-Atik; Amal T. Abushaaban; O. A. Embaby; Abdelfattah A. El-Atik

doi:10.3934/math.2025100

AIMS Mathematics

2025, Volume 10, Issue 2: 2131-2162. doi: 10.3934/math.2025100

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Research article

Modern classes of fuzzy $ \alpha $-covering via rough sets over two distinct finite sets

Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

Received: 08 November 2024 Revised: 03 January 2025 Accepted: 15 January 2025 Published: 08 February 2025
MSC : 54A40, 54C55, 54D20, 60L20

Following the research of Yang and Atef proposing new classes of fuzzy $ \beta $-covering via rough sets types over 2-featured universes, we present some modern classes of fuzzy $ \alpha $-covering via rough sets over two distinct finite sets using fuzzy $ \alpha $-neighborhoods for two distinct points over 2-distinct finite universes. Throughout this research, we present the ideas of the fuzzy $ \alpha $-neighborhood system and the fuzzy $ \alpha $-neighborhood for two distinct points over two distinct finite sets and investigate the relations of the fuzzy $ \alpha $-neighborhood system, fuzzy $ \alpha $-minimal and $ \alpha $-maximal descriptions over two distinct finite sets. Moreover, some kinds of fuzzy $ \alpha $-neighborhoods are proposed. In addition, some new types of fuzzy $ \alpha $-coverings over two finite sets are established. Finally, numerous topological characteristics of fuzzy $ \alpha $-covering via rough set types are investigated.
- rough sets,
- fuzzy $ \alpha $-neighborhoods,
- fuzzy $ \alpha $-coverings
Citation: Amal T. Abushaaban, O. A. Embaby, Abdelfattah A. El-Atik. Modern classes of fuzzy $ \alpha $-covering via rough sets over two distinct finite sets[J]. AIMS Mathematics, 2025, 10(2): 2131-2162. doi: 10.3934/math.2025100

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Abstract

Following the research of Yang and Atef proposing new classes of fuzzy $ \beta $-covering via rough sets types over 2-featured universes, we present some modern classes of fuzzy $ \alpha $-covering via rough sets over two distinct finite sets using fuzzy $ \alpha $-neighborhoods for two distinct points over 2-distinct finite universes. Throughout this research, we present the ideas of the fuzzy $ \alpha $-neighborhood system and the fuzzy $ \alpha $-neighborhood for two distinct points over two distinct finite sets and investigate the relations of the fuzzy $ \alpha $-neighborhood system, fuzzy $ \alpha $-minimal and $ \alpha $-maximal descriptions over two distinct finite sets. Moreover, some kinds of fuzzy $ \alpha $-neighborhoods are proposed. In addition, some new types of fuzzy $ \alpha $-coverings over two finite sets are established. Finally, numerous topological characteristics of fuzzy $ \alpha $-covering via rough set types are investigated.

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