Novel decision-making framework based on complex q-rung orthopair fuzzy information

Assessing uncertainty in decision-making is a major challenge for Decision-Makers (DMs), and the q-Rung Orthopair Fuzzy Set (q-ROFS) as the direct extension of Intuitionistic Fuzzy Set (IFS) and Pythagorean Fuzzy Set (PFS) play a crucial role in this aspect. The Complex q-Run Orthopair Fuzzy Set (Cq-ROFS) is a strong tool to deal with imprecision, vagueness, and fuzziness by expanding the scope of Membership Degree (MD) and Non-Membership Degree (NMD) of q-ROFS from real to complex unit disc. In this paper, we develop some new Cq-ROF Hamacher Aggregation Operators (AOs), i.e., the Cq-ROF Hamacher Weighted Averaging (Cq-ROFHWA) operator, the Cq-ROFH Weighted Geometric (Cq-ROFHWG) operator, the Cq-ROFH Ordered Weighted Averaging (Cq-ROFHOWA) operator, and the Cq-ROFH Ordered Weighted Geometric (Cq-ROFHOWG) operator. Subsequently, we establish a novel Cq-ROF graph framework based on the Hamacher operator called Cq-ROFH Graphs (Cq-ROFHGs) and evaluate its energy and Randi c energy. In particular, we compute the energy of a splitting Cq-ROFHG and shadow Cq-ROFHG. Further, we describe the notions of Cq-ROFH digraphs (Cq-ROFHDGs). Moreover, an algorithm is given to solve Multiple Attribute Group Decision-Making (MAGDM) problems and the main steps are discussed clearly. Finally, a numerical instance related to the Facade Clothing Systems (FCS) selection is presented to show the e ectiveness of the developed concepts in decision-making circumstances. In order to verify the e ectiveness of our proposed scheme, a comparative analysis with previous approaches is provided.