In this paper, we introduce the concept of the circular complex $q$-rung orthopair fuzzy set (CC$q$-ROFS) as a novel generalization that unifies the existing frameworks of circular complex intuitionistic fuzzy sets (CCIFSs) and complex $q$-rung orthopair fuzzy sets. If $q = 2$, the structure is referred to as a circular complex Pythagorean fuzzy set, and if $q = 3$, it is called a circular complex Fermatean fuzzy set. The proposed approach extends the Gaussian-based framework to the CC$q$-ROFSs, aiming to achieve a smoother and statistically meaningful representation of uncertainty. Within this setting, new Gaussian-based aggregation operators for CC$q$-ROFSs are constructed by employing the Gaussian triangular norm and conorm. Furthermore, Gaussian-weighted arithmetic and Gaussian-weighted geometric aggregation operators are formulated to enable consistent integration of membership and non-membership information for fuzzy modeling and decision-making.

翻译：本文引入了圆形复$q$阶正交模糊集（CC$q$-ROFS）的概念，作为一种新颖的推广，统一了现有圆形复直觉模糊集（CCIFSs）与复$q$阶正交模糊集的框架。当$q = 2$时，该结构称为圆形复毕达哥拉斯模糊集；当$q = 3$时，则称为圆形复费马模糊集。所提出的方法将基于高斯的框架扩展至CC$q$-ROFS，旨在实现对不确定性的更平滑且具有统计意义的表征。在此框架下，通过采用高斯三角模与余模，构建了适用于CC$q$-ROFS的基于高斯的聚合算子。此外，还提出了高斯加权算术与高斯加权几何聚合算子，以实现隶属度与非隶属度信息在模糊建模与决策中的一致集成。