New generalizations of circular complex fuzzy sets and Gaussian weighted aggregation operators
Yelda Gülfırat, Mehmet Ünver
TL;DR
This work generalizes circular complex fuzzy sets to CC$q$-ROFS, unifying circular complex intuitionistic fuzzy sets and complex $q$-rung orthopair fuzzy sets, with CCPFS ($q=2$) and CCFFS ($q=3$) as special cases. It introduces Gaussian-based Archimedean $t$-norms and $t$-conorms to enable smooth, statistically meaningful aggregation on CC$q$-ROFS and CC$q$-ROFV, including real and imaginary membership components and radii. The paper defines algebraic operators $A_1 ⊕_q A_2$, $A_1 ⊗_q A_2$, $λ_q A_1$, and $A_1^{λ_q}$ with a radius combination $Z(r_1,r_2)$, and constructs Gaussian-weighted aggregation operators CC$q$-ROFWA and CC$q$-ROFWG for fusing CC$q$-ROFVs. The framework recovers CCPFS and CCFFS as special cases and offers practical tools for smoother uncertainty representation in fuzzy decision-making and pattern recognition tasks.
Abstract
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.