Rough and T-Rough Sets Arising from Intuitionistic Fuzzy Ideals in BCK-Algebras

Kholood M. Alsager and Sheza M. El-Deeb ()
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Kholood M. Alsager: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Sheza M. El-Deeb: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

Mathematics, 2024, vol. 12, issue 18, 1-24

Abstract: This paper presents the novel concept of rough intuitionistic fuzzy ideals within the realm of BCK-algebras and investigates their fundamental properties. Furthermore, we introduce a set-valued homomorphism over a BCK-algebra, laying the foundation for the establishment of T-rough intuitionistic fuzzy ideals. The characterization of these innovative ideals is accomplished by employing the ( α , β ) -cut of intuitionistic fuzzy sets in the context of BCK-algebras.

Keywords: fuzzy set; rough set; fuzzy logic; T-rough set; intuitionistic fuzzy set; lower approximation; upper approximation; fuzzy ideal; rough intuitionistic fuzzy ideal (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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