An Approach for Hybridizing N-Subalgebra with Quantified Neutrosophic Set using G-Algebra

Neha Andaleeb Khalid, Department of Mathematics, University of Management and Technology, C-II, Johar Town, Lahore, 54700, PakistanFollow
Muhammad Saeed, Department of Mathematics, University of Management and Technology, C-II, Johar Town, Lahore, 54700, PakistanFollow

ORCID

Neha Andaleeb Khalid: https://orcid.org/0009-0006-2245-7601

Muhammad Saeed: https://orcid.org/0000-0002-7284-6908

Article Type

Article

Abstract

Neutrosophic sets are a generalized form of fuzzy sets as well as intuitionistic fuzzy sets, as they address the uncertainty factor as an independent component along with truthfulness and falsity. However, traditional neutrosophic approaches often struggle with effectively managing and quantifying indeterminate elements in complex algebraic structures. To address this limitation, this paper employs an expanded version of the neutrosophic set, incorporating a subalgebra. The proposed research is multifaceted: firstly, the new concept of N-Subalgebra (NSU) is proposed. This is the modified setting in the family of subalgebras whose proposed name is the representation of the author's initial name. Secondly, the hybridization is called Quantified Neutrosophic N-Subalgebra. Q^tNNSU of NSU is established with the modified version of the neutrosophic set, which is Quantified quantified neutrosophic set Q^t NS. This novel approach to hybridization is the combination of the properties related to NSU in the Q^t NS's setting. Thirdly, the operations of P-Union, R-Union, P-Intersection, and R-Intersection are developed for the Q^tNNSU and presented as P_Q^t Union, R_Q^t Union, P_Q^t-Intersection and, R_Q^t-Intersection. Furthermore, the concepts of upper bounds, lower bounds, including upper-level subalgebras, as well as lower-level subalgebras in the environment of Q^tNNSU are developed. The proposed study is an advancement in the field of neutrosophic set theory-related algebraic structures.

Keywords

Algebraic structures, Indeterminacy management, Uncertainty quantification, Hybrid set theory, Neutrosophic operations

How to Cite

Khalid, Neha Andaleeb and Saeed, Muhammad (2025) "An Approach for Hybridizing N-Subalgebra with Quantified Neutrosophic Set using G-Algebra," Neutrosophic Systems with Applications: Vol. 25: Iss. 1, Article 2. DOI: https://doi.org/10.61356/j.nswa.2025.25411