Bipolar-Valued Intuitionistic Fuzzy Positive Implicative Ideals in $\mathcal{BCK}$-Algebras

Authors

  • D. Ramesh Koneru Lakshmaiah Education Foundation
  • Shake Baji Sir C.R. Reddy College of Engineering
  • Aiyared Iampan Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand https://orcid.org/0000-0002-0475-3320
  • R. Durga Prasad KG Reddy College of Engineering and Technology
  • B. Satyanarayana Acharya Nagarjuna University

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i1.5699

Keywords:

Bipolar-valued fuzzy set (BPVFS), bipolar-valued intuitionistic fuzzy set (BPVIFS), bipolar-valued intuitionistic fuzzy ideal (BPVIFI), bipolar-valued intuitionistic fuzzy positive implicative ideal (BPVIFPII)

Abstract

This study develops a novel framework for bipolar-valued intuitionistic fuzzy positive implicative ideals (BPVIFPIIs) in BCK-algebras by integrating bipolar-valued intuitionistic fuzzy set theory with algebraic structures. The primary objective is to define and explore the properties of BPVIFPIIs in BCK-algebras, providing rigorous theoretical foundations supported by illustra-
tive examples. Key conditions under which a bipolar-valued intuitionistic fuzzy set qualifies as a BPVIFPII are established. The findings reveal significant connections between BPVIFPIIs and other fuzzy ideals, highlighting their role in advancing the understanding of uncertainty and algebraic reasoning. This research opens avenues for further exploration of bipolar fuzzy structures in algebra and their practical implications in decision-making processes involving uncertain data.

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Published

2025-01-31

Issue

Section

Nonlinear Analysis

How to Cite

Bipolar-Valued Intuitionistic Fuzzy Positive Implicative Ideals in $\mathcal{BCK}$-Algebras. (2025). European Journal of Pure and Applied Mathematics, 18(1), 5699. https://doi.org/10.29020/nybg.ejpam.v18i1.5699