Binary relations applied to the fuzzy substructures of quantales under rough environment

Saqib Mazher Qurashi; Bander Almutairi; Qin Xin; Rani Sumaira Kanwal; null Aqsa

doi:10.1515/dema-2023-0109

Binary relations applied to the fuzzy substructures of quantales under rough environment

Saqib Mazher Qurashi, Bander Almutairi, Qin Xin, Rani Sumaira Kanwal, Aqsa

Research output: Contribution to journal › Article › peer-review

Abstract

Binary relations (BIRs) have many applications in computer science, graph theory, and rough set theory. This study discusses the combination of BIRs, fuzzy substructures of quantale, and rough fuzzy sets. Approximation of fuzzy subsets of quantale with the help of BIRs is introduced. In quantale, compatible and complete relations in terms of aftersets and foresets with the help of BIRs are defined. Furthermore, we use compatible and complete relations to approximate fuzzy substructures of quantale, and these approximations are interpreted by aftersets and foresets. This concept generalizes the concept of rough fuzzy quantale. Finally, using BIRs, quantale homomorphism is used to build a relationship between the approximations of fuzzy substructures of quantale and the approximations of their homomorphic images.

Original language	English
Article number	20230109
Number of pages	22
Journal	Demonstratio Mathematica
Volume	57
Issue number	1
DOIs	https://doi.org/10.1515/dema-2023-0109
Publication status	Published - 2024

Keywords

binary relations
fuzzy substructures in quantale
rough fuzzy sets
compatible relations

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Qurashi et al Binary relations applied to the fuzzyFinal published version, 4.36 MBLicence: CC BY

https://doi.org/10.1515/dema-2023-0109

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abstract = "Binary relations (BIRs) have many applications in computer science, graph theory, and rough set theory. This study discusses the combination of BIRs, fuzzy substructures of quantale, and rough fuzzy sets. Approximation of fuzzy subsets of quantale with the help of BIRs is introduced. In quantale, compatible and complete relations in terms of aftersets and foresets with the help of BIRs are defined. Furthermore, we use compatible and complete relations to approximate fuzzy substructures of quantale, and these approximations are interpreted by aftersets and foresets. This concept generalizes the concept of rough fuzzy quantale. Finally, using BIRs, quantale homomorphism is used to build a relationship between the approximations of fuzzy substructures of quantale and the approximations of their homomorphic images.",

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T1 - Binary relations applied to the fuzzy substructures of quantales under rough environment

AU - Qurashi, Saqib Mazher

AU - Almutairi, Bander

AU - Xin, Qin

AU - Kanwal, Rani Sumaira

AU - Aqsa, null

PY - 2024

Y1 - 2024

N2 - Binary relations (BIRs) have many applications in computer science, graph theory, and rough set theory. This study discusses the combination of BIRs, fuzzy substructures of quantale, and rough fuzzy sets. Approximation of fuzzy subsets of quantale with the help of BIRs is introduced. In quantale, compatible and complete relations in terms of aftersets and foresets with the help of BIRs are defined. Furthermore, we use compatible and complete relations to approximate fuzzy substructures of quantale, and these approximations are interpreted by aftersets and foresets. This concept generalizes the concept of rough fuzzy quantale. Finally, using BIRs, quantale homomorphism is used to build a relationship between the approximations of fuzzy substructures of quantale and the approximations of their homomorphic images.

AB - Binary relations (BIRs) have many applications in computer science, graph theory, and rough set theory. This study discusses the combination of BIRs, fuzzy substructures of quantale, and rough fuzzy sets. Approximation of fuzzy subsets of quantale with the help of BIRs is introduced. In quantale, compatible and complete relations in terms of aftersets and foresets with the help of BIRs are defined. Furthermore, we use compatible and complete relations to approximate fuzzy substructures of quantale, and these approximations are interpreted by aftersets and foresets. This concept generalizes the concept of rough fuzzy quantale. Finally, using BIRs, quantale homomorphism is used to build a relationship between the approximations of fuzzy substructures of quantale and the approximations of their homomorphic images.

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KW - compatible relations

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DO - 10.1515/dema-2023-0109

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JO - Demonstratio Mathematica

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Binary relations applied to the fuzzy substructures of quantales under rough environment

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Keywords

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