Research Article On q-Rung Orthopair Fuzzy Subgroups Asima Razzaque 1 and Abdul Razaq 2 1 Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University Al Ahsa, Al Hofuf, Saudi Arabia 2 Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan Correspondence should be addressed to Asima Razzaque; arazzaque@kfu.edu.sa and Abdul Razaq; abdul.razaq@ue.edu.pk Received 18 April 2022; Accepted 23 May 2022; Published 6 June 2022 Academic Editor: Muhammad Gulzar Copyright © 2022 Asima Razzaque and Abdul Razaq. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The q-rung orthopair fuzzy environment is an innovative tool to handle uncertain situations in various decision-making problems. In this work, we characterize the idea of a q-rung orthopair fuzzy subgroup and examine various algebraic attributes of this newly defined notion. We also present q-rung orthopair fuzzy coset and q-rung orthopair fuzzy normal subgroup along with relevant fundamental theorems. Moreover, we introduce the concept of q-rung orthopair fuzzy level subgroup and proved related results. At the end, we explore the consequence of group homomorphism on the q-rung orthopair fuzzy subgroup. 1. Introduction In classical fuzzy set theory, a fuzzy subset of a crisp set S is represented by a function from S to ½0, 1 ⊆ ℝ. The inequal- ities and equations are used to define operations and charac- teristic. The original notion of the fuzzy set was proposed in 1965 by Zadeh [1]. Since then, it has been used in almost every field of science especially where mathematical logic and set theory are significantly involved. A fuzzy subset R of a crisp set S is an object fs, μ R ðsÞ: s ∈ Sg such that μ R : S ⟶ ½0, 1 is called membership mapping of R and μ R ðs Þ is known as a degree of membership of s in R. One can see that fuzzy sets are the extensions of characteristic func- tions of classical sets, by expanding the range of the function from f0, 1g to ½0, 1. After the proposal of fuzzy sets, a lot of theories have been put forward to handle uncertain and imprecision circumstances. Some of these theories are expansions of fuzzy sets, whereas others strive to cope with uncertainties in another appropriate manner. Atanassov [2] introduced an intuitionistic fuzzy set (IFS) which is the generalization of fuzzy set. An intuitionistic fuzzy subset R of a crisp set S is an object fs, μ R ðsÞ, ν R ðsÞ: s ∈ Sg, where μ R : S ⟶ ½0, 1 and ν R : S ⟶ ½0, 1 are membership and nonmembership functions, respectively, such that μ R ðsÞ + ν R ðsÞ ≤ 1 for all s ∈ S. Compared with classical fuzzy sets, the positive and negative membership functions of intuitio- nistic fuzzy sets ensure its effective handling of uncertain and vague situations in physical problem, especially in the field of decision-making [3–6]. In 2013, Yager [7] general- ized intuitionistic fuzzy sets by presenting the idea of Pythagorean fuzzy set (PFS). The Pythagorean fuzzy subset R of a crisp set S is an object fs, μ R ðsÞ, ν R ðsÞ: s ∈ Sg, where μ R : S ⟶ ½0, 1 and ν R : S ⟶ ½0, 1 are membership and nonmembership functions, respectively, such that ðμ R ðsÞÞ 2 + ðν R ðsÞÞ 2 ≤ 1 for all s ∈ S. This concept is designed to con- vert uncertain and vague environment in the form of math- ematics and to find more effective solutions of such real- world problems [8–11]. Although Pythagorean fuzzy subsets solve different types of real-life problems in an efficient way but even then, there is a room for improvement because there exists so many cases where Pythagorean fuzzy subsets fail to work. For example, if positive and negative member- ship values proposed by a decision-maker are 0.75 and 0.85, respectively, then ð0:75 Þ 2 + ð0:85 Þ 2 >1; therefore, Pythagorean fuzzy subsets fail to deal with such problems. In order to find a reasonable solution of such kinds of situ- ations, Yager defines the notion of q-rung orthopair fuzzy set (q-ROFS), where q is a natural number [12]. The q -rung orthopair fuzzy subset R of a crisp set S is an object fs, μ R ðsÞ, ν R ðsÞ: s ∈ Sg, where μ R : S ⟶ ½0, 1 and Hindawi Journal of Function Spaces Volume 2022, Article ID 8196638, 9 pages https://doi.org/10.1155/2022/8196638