Implicative and Positive Implicative Ideals of Neutrosophic INK-algebras

Authors

  • Remala Mounikalakshmi Department of Engineering Mathematics, College of Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Andhra 444 Pradesh 522302, India
  • Eswarlal Tamma Department of Engineering Mathematics, College of Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Andhra 444 Pradesh 522302, India
  • Venkata Kalyani Uppuluri Freshman Engineering Department, NRI Institute of Technology, Pothavarapadu, Nunna, Agiripalli, Vijayawada-521212, India
  • Aiyared Iampan Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand https://orcid.org/0000-0002-0475-3320
  • Srinivasa Rao Department of Engineering Mathematics, College of Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram, Andhra 444 Pradesh 522302, India

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6226

Keywords:

INK-algebra, fuzzy set, neutrosophic set, implicative ideal, positive implicative ideal, fuzzy implicative ideal, fuzzy positive implicative ideal, neutrosophic implicative ideal, neutrosophic positive implicative ideal

Abstract

This paper introduces and develops the concepts of implicative and positive implicative ideals within the framework of INK-algebras. These notions are subsequently extended to fuzzy and neutrosophic contexts, resulting in the definitions of fuzzy implicative ideals (FMI), fuzzy positive implicative ideals (FPMI), neutrosophic implicative ideals (NII), and neutrosophic positive implicative ideals (NPII). The structural properties of these ideals are investigated, including their behavior under intersection and union, where it is shown that intersection preserves the respective implicative properties, while union does not in general. Furthermore, we establish that the homomorphic pre-images of these ideals also preserve their respective fuzzy and neutrosophic implicative structures. The results contribute to a deeper understanding of ideal theory in INK-algebras under uncertainty, and open pathways for applications in fuzzy logic and neutrosophic systems.

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Algebra

License

Copyright (c) 2025 Remala Mounikalakshmi, Eswarlal Tamma, Venkata Kalyani Uppuluri, Aiyared Iampan, Srinivasa Rao

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How to Cite

Implicative and Positive Implicative Ideals of Neutrosophic INK-algebras. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6226. https://doi.org/10.29020/nybg.ejpam.v18i4.6226