A New Approach of Complex Fuzzy Ideals in BCK/BCI-Algebras

Manivannan Balamurugan (), Thukkaraman Ramesh, Anas Al-Masarwah and Kholood Alsager ()
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Manivannan Balamurugan: Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600 062, India
Thukkaraman Ramesh: Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600 062, India
Anas Al-Masarwah: Department of Mathematics, Faculty of Science, Ajloun National University, P.O. Box 43, Ajloun 26810, Jordan
Kholood Alsager: Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia

Mathematics, 2024, vol. 12, issue 10, 1-18

Abstract: The concept of complex fuzzy sets, where the unit disk of the complex plane acts as the codomain of the membership function, as an extension of fuzzy sets. The objective of this article is to use complex fuzzy sets in BCK/BCI-algebras. We present the concept of a complex fuzzy subalgebra in a BCK/BCI-algebra and explore their properties. Furthermore, we discuss the modal and level operators of these complex fuzzy subalgebras, highlighting their importance in BCK/BCI-algebras. We study various operations, and the laws of a complex fuzzy system, including union, intersection, complement, simple differences, and bounded differences of complex fuzzy ideals within BCK/BCI-algebras. Finally, we generate a computer programming algorithm that implements our complex fuzzy subalgebras/ideals in BCK/BCI-algebras procedure for ease of lengthy calculations.

Keywords: BCK/BCI-algebras; fuzzy logic; complex fuzzy set; complex fuzzy subalgebra; complex fuzzy ideal (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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