Volume 27 • Issue 2 • PP: 373-391 • 2026
Enforcement of q-Rung Orthopair Fuzzy Subsets to Q-Ideals
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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 independen 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.
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References
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