Enforcement of q-Rung Orthopair Fuzzy Subsets to Q-Ideals
Mohammad Hamidi1,∗, Sirous Jahanpanah1, Florentin Smarandache2
1Department of Mathematics, Payame Noor University (PNU), P. O. Box 19395-4697, Tehran, Iran
2Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA
Emails: m.hamidi@pnu.ac.ir; s.jahanpanah@pnu.ac.ir; smarand@unm.edu
Abstract
This paper presents an innovative generalization of intuitionistic fuzzy Q-subalgebras (IF-Q-S) by incorpo-
rating 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.
Keywords: Q-algebra; q-Rung Orthopair fuzzy set; q-Rung Orthopair fuzzy Q-algebra; q-Rung Orthopair
fuzzy Q-ideal