Branch Mathematics and Statistics Faculty and Staff Publications

Document Type

Article

Publication Date

2026

Abstract

This paper presents an innovative generalization of intuitionistic fuzzy Q-subalgebras (IF-Q-S) by incorporating the structure of q-Rung Orthopair fuzzy sets (q-ROFS), which are distinguished by their independent membership and non-membership functions. It inserts and investigates q-Rung Orthopair fuzzy Q-subalgebras (q-ROFQ-S), demonstrating that this model is equivalent to a combination of a fuzzy Q-subalgebra (F-Q-S) and an anti-fuzzy Q-subalgebra (AF-Q-S). The study’s notable contributions include the definition of the nil radical and an exploration of its properties under homomorphisms. Additionally, it establishes that the union of q-ROFQ-subalgebras can itself form such a subalgebra under particular commutative conditions. Expanding the concept to the realm of ideals, the paper defines q-Rung Orthopair fuzzy Q-ideals (q-ROFQ-I) and proves that every q-regular q-ROFQ-S is inherently a q-ROFQ-I. This work offers a robust and versatile algebraic framework for addressing approximation in complex nonlinear systems.

Language (ISO)

English

Keywords

Q-algebra, q-Rung Orthopair fuzzy set, q-Rung Orthopair fuzzy Q-algebra, q-Rung Orthopair fuzzy Q-ideal

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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