International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3755 2020 2020 Department of Mathematics, Faculty of Science, Ajloun National University, P.O. Box 43, Ajloun 26810, Jordan Manivannan Manivannan Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R\&D Institute of Science and Technology, Chennai 600062, Tamil Nadu, India Manivannan Balamurugan Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, Tamil Nadu, India; Department of Mathematics, Sri Vidya Mandir Arts & Science College (Autonomous), Uthangarai 636902, Tamil Nadu, India Thukkaraman Ramesh Department of Mathematics, Faculty of Science, Jadara University, Irbid 21110, Jordan Majdoleen Abuqamar Department of Computer Science, College of Engineering and InformationTechnology, Onaizah Colleges, Al-Qassim 56447, Saudi Arabia Maryam Abdullah Alshayea 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. 2025 2025 26 48 10.54216/IJNS.260303 https://www.americaspg.com/articleinfo/21/show/3755