Volume 26 , Issue 3 , PP: 26-48, 2025 | Cite this article as | XML | PDF | Full Length Article
Anas Al-Masarwah 1 , Manivannan Balamurugan 2 * , Thukkaraman Ramesh 3 , Majdoleen Abuqamar 4 , Maryam Abdullah Alshayea 5
Doi: https://doi.org/10.54216/IJNS.260303
A complex linear Diophantine fuzzy (CLDF) set extends a linear Diophantine fuzzy set (LDFS) by handling uncertainty with complex-valued membership degrees within a unit disc. In this paper, we combine the notions of LDFS, BCK-algebra, and complex fuzzy set (CFS) to preface and elaborate the innovative concepts of CLDF subalgebras (CLDF − Subs), CLDF ideals (CLDF − Ids), CLDF implicative ideals (CLDF − IIds), and CLDF positive implicative ideals (CLDF − PIIds) in BCK-algebras, and probe their fundamental characteristics. These new notations of certain kinds of algebraic substructures in BCK-algebras serve as a bridge among CLDFS, crisp set, and BCK-algebra and also demonstrate the influence of the CLDFS on a BCK-algebra. Moreover, we examine some illustrative examples and prevalent features of these innovative notions in detail. Finally, characterizations of these intricate fuzzy structures are given, and related results for ideals, implicative ideals, and positive implicative ideals in the view of CLDFSs are obtained.
BCK-algebra , Complex linear Diophantine fuzzy set , Complex linear Diophantine fuzzy sub-algebra , Complex linear Diophantine fuzzy idea
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