Sharif University of TechnologyScientia Iranica1026-309830420230801Novel decision-making framework based on complex q-rung orthopair fuzzy information145014792229210.24200/sci.2021.55413.4209ENM. AkramDepartment of Mathematics, University of the Punjab, New Campus, Lahore, Pakistanhttps://orcid.org/00S. NazDepartment of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistanorcid.org/0000-0001-6550-9607F. ZiaaDepartment of Mathematics, Minhaj University, Lahore, PakistanJournal Article20200207The q-rung orthopair fuzzy sets (q-ROFSs) are increasingly valuable to express fuzzy and vague<br />information, as the generalization of intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets<br />(PFSs). In this paper, we propose complex $q$-rung orthopair fuzzy sets (C$q$-ROFSs) as a new tool to deal with vagueness, uncertainty and fuzziness by extending the range of membership and non-membership function of $q$-ROFS from real to complex number with the unit disc.<br />We develop some new complex $q$-rung orthopair fuzzy Hamacher operations and complex $q$-rung orthopair fuzzy Hamacher aggregation operators, i.e., the complex $q$-rung orthopair fuzzy Hamacher weighted average (C$q$-ROFHWA) operator, and the complex $q$-rung orthopair fuzzy Hamacher weighted geometric (C$q$-ROFHWG) operator. Subsequently, we introduce the innovative concept of a complex $q$-rung orthopair fuzzy graphs based on Hamacher operator called complex $q$-rung orthopair fuzzy Hamacher graphs (C$q$-ROFHGs) and determine its energy and Randi\'{c} energy.<br />In particular, we present the energy of a splitting C$q$-ROFHG and shadow C$q$-ROFHG. Further, we describe the notions of complex $q$-rung orthopair fuzzy Hamacher digraphs (C$q$-ROFHDGs).<br />Finally, a numerical instance related to the facade clothing systems selection is presented to demonstrate the validity of the proposed concepts in decision making (DM).https://scientiairanica.sharif.edu/article_22292_429ec75a69a18d5362002dc3d04cc845.pdf