Affiliations: [a] Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
| [b] Department of Mathematics, University of Jeddah, College of Science, Jeddah, Saudi Arabia
| [c] Department of Mathematics, Faculty of Sciences, Çankiri Karatekin University, Çankiri, Turkey
Correspondence:
[*]
Corresponding author. Faruk Karaaslan, Department of Mathematics, Faculty of Sciences, Çankiri Karatekin University, 18100, Çankiri, Turkey. E-mail: [email protected].
Abstract: A q-rung orthopair fuzzy set (q-ROFS) is more practical and powerful than intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS) to model uncertainty in various decision-making problems. In this research article, we introduce the notion of q-rung orthopair fuzzy Hamacher graphs (q-ROFHGs). We utilize the Hamacher operators because they are flexible and parameterized in decision making. We determine the energy of q-ROFHGs as well as the energy of splitting and shadow q-ROFHGs. In addition, we propose the Randić energy of q-ROFHG and its some substantial results. Further, we present the idea of q-rung orthopair fuzzy Hamacher digraphs (q-ROFHDGs). We solve a decision-making numerical example related to the selection of best housing society for investment by calculating the energy and Randić energy of q-ROFHDGs and an algorithm to exhibit the applicability of the presented concepts in decision making. Finally, we present the conclusion.
