Exploring the Structural Aspects of Interval-Valued  Intuitionistic Neutrosophic Fuzzy Ẑ-Subalgebra

K. P. Shanmugapriya; P. Hemavathi; M. Al-Labadi; S. Khalil; A. E. Kadhm; Qays H. Imran

Authors

K. P. Shanmugapriya Department of Mathematics, Saveetha Institute of Medical and Technical Sciences (SIMATS), Saveetha School of Engineering, Thandalam, 602 105, India.
P. Hemavathi Department of Mathematics, Saveetha Institute of Medical and Technical Sciences (SIMATS), Saveetha School of Engineering, Thandalam, 602 105, India.
M. Al-Labadi Department of Mathematics, Faculty of Arts and Sciences, University of Petra, Amman,
S. Khalil Department of Mathematics, College of Science, University of Basrah, Basrah 61004, Iraq.
A. E. Kadhm Technical Engineering College-Baghdad, Middle Technical University, Baghdad, Iraq.
Qays H. Imran Department of Mathematics, College of Education for Pure Science, Al-Muthanna University, Samawah, Iraq.

Keywords:

Fuzzy set, Ẑ-subalgebra, intuitionistic fuzzy Ẑ-subalgebra, interval-valued fuzzy Ẑ-subalgebra, neutrosophic fuzzy Ẑ-subalgebra.

Abstract

The article develops an updated methodology of interval-valued intuitionistic neutrosophic sets
(IVINS) based on Ẑ-algebra theoretical structures. The new method presents an advanced solution to real-world
uncertainties alongside inconsistent and indeterminate states found during decision-making and problem
solving activities. The investigation follows up by proving fundamental principles for Ẑ-algebra under this
neutrosophic extension. Researchers have deeply studied homomorphism properties and Cartesian product
operations of interval-valued intuitionistic neutrosophic sets contained in Ẑ-algebras. Research applications
of fuzzy set theory span multiple domains that include real-world, theoretical, and imaginary contexts. Multiple
algebraic structures such as BCK/BCI-algebras, UP-algebras, and B-algebras, alongside others have validated
fuzzy sets mathematically, thus proving their extensive applicability in abstract mathematical systems.

DOI 10.5281/zenodo.17162790