An Innovative Perspective on Bipolar Fuzzy Fantastic Ideals in BCK/BCI-Algebras

Authors

  • M. Balamurugan Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R\&D Institute of Science and Technology, Chennai, Tamil Nadu, India
  • Khalil H. Hakami Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Kingdom of Saudi Arabia
  • Moin A. Ansari Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Kingdom of Saudi Arabia
  • K. Loganathan Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur-303007, India

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i4.5527

Keywords:

BCK/BCI-algebras, fuzzy logic, bipolar fuzzy ideal $(\mathcal{BFI})$, bipolar fuzzy fantastic ideal $\mathsf{(\mathcal{BFFI})}$,  $(\in, \in \vee (\varphi^{\divideontimes}, \check{q_{\varphi}}))$-$\mathcal{BFI}$, $(\in, \in \vee (\varphi^{\divideontimes}, \check{q_{\varphi}}))$-$\mathcal{BFFI}$

Abstract

In this paper, we propose the concept of $(\in, \in \vee (\varphi^{\divideontimes}, \check{q_{\varphi}}))$-bipolar fuzzy ideals in BCK/BCI-algebras. We show that an $(\in, \in \vee \check{q_{\varphi}})$-bipolar fuzzy ideal is an $(\in, \in \vee (\varphi^{\divideontimes}, \check{q_{\varphi}}))$-bipolar fuzzy ideal. For a BCK/BCI-algebra, it has been shown that an $(\in, \in \vee (\varphi^{\divideontimes}, \check{q_{\varphi}})$-bipolar fuzzy ideal is an $(\in, \in \vee \check{q})$-bipolar fuzzy ideal of $\check{\aleph}$, but not conversely, and then an example is given. We introduce the concept of $(\in, \in \vee (\varphi^{\divideontimes}, \check{q_{\varphi}}))$-bipolar fuzzy fantastic ideals in BCK/BCI-algebras. It has been shown that an $(\in, \in \vee (\varphi^{\divideontimes}, \check{q_{\varphi}}))$-bipolar fuzzy fantastic ideal is an $(\in, \in)$-bipolar fuzzy ideal in BCK/BCI-algebras. Furthermore, the connection between $(\in, \in \vee (\varphi^{\divideontimes}, \check{q_{\varphi}}))$-bipolar fuzzy fantastic ideals and fantastic ideals are established.

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Published

2024-10-31

Issue

Vol. 17 No. 4: (October 2024)

Section

Nonlinear Analysis

License

Copyright (c) 2024 M. Balamurugan, Khalil H. Hakami, Moin A. Ansari, K. Loganathan

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How to Cite

An Innovative Perspective on Bipolar Fuzzy Fantastic Ideals in BCK/BCI-Algebras. (2024). European Journal of Pure and Applied Mathematics, 17(4), 3973-3983. https://doi.org/10.29020/nybg.ejpam.v17i4.5527