Novel Decision Making Framework Based on Complex q-Rung Orthopair Fuzzy Information

Document Type : Article

Authors

1 Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan

2 Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan

3 Department of Mathematics, Minhaj University, Lahore, Pakistan

Abstract

The q-rung orthopair fuzzy sets (q-ROFSs) are increasingly valuable to express fuzzy and vague
information, as the generalization of intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets
(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.
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.
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).
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).

Keywords


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