Affiliations: [a] Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
| [b] Department of Mathematics, Division of Science and Technology, University of Education, Lahore, Pakistan
| [c] School of Mathematics, Minhaj University, Lahore, Pakistan
Correspondence:
[*]
Corresponding author. Muhammad Akram, Department of Mathematics, University of the Punjab, New Campus, Lahore, P.O. Box 54590, Pakistan. E-mail: m.akram@pucit.edu.pk.
Abstract: q-Rung orthopair fuzzy sets (q-ROFSs), originally proposed by Yager, can powerfully modify the range of indication of decision information by changing a parameter q based on the different hesitation degree, and the dual hesitant q-rung orthopair fuzzy set (DHq-ROFS), a new technique to consider human’s hesitance, can be more substantial of dealing with real multi-attribute decision making (MADM) problems. Inspired by DHq-ROFSs, in this article, we extend the concept of q-rung orthopair fuzzy graphs to dual hesitant q-rung orthopair fuzzy context and introduce the innovative concept of a dual hesitant q-rung orthopair fuzzy graphs based on Hamacher operator called dual hesitant q-rung orthopair fuzzy Hamacher graphs (DHq-ROFHGs). We propose the new concepts of geometric-arithmetic energy and atom bond connectivity energy of a DHq-ROFHG and determine its upper and lower bounds. Moreover, on the basis of the proposed concept of DHq-ROFHGs, we introduce a new approach to solve the MADM problems with dual hesitant q-rung orthopair fuzzy information. At the end, we give a numerical model related to the selection of most significant defensive factor to illustrate the applicability of the developed approach, and exhibit its viability. Comparative analysis is conducted and the superiorities are illustrated.
Keywords: Dual hesitant q-rung orthopair fuzzy graph, Hamacher operator, Geometric-arithmetic energy, Atom bond connectivity energy, Multi-attribute decision making
