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Dual Hesitant q-Rung Orthopair Fuzzy Hamacher Graphs with Application
Muhammad Akram, Sumera Naz and Faiza Ziaa

Yager’s q-rung orthopair fuzzy sets (q-ROFSs) can powerfully modify the range of indication of choice data 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. In this paper, we introduce the innovative concept of dual hesitant q-rung orthopair fuzzy graphs based on Hamacher operator called dual hesitant q-rung orthopair fuzzy Hamacher graphs (DHq-ROFHGs) and determine its energy and Randić energy. In particular, we present the energy of a generalized splitting DHq-ROFHG and generalized shadow DHq-ROFHG. Finally, a numerical instance related to the potential evaluation of emerging technology commercialization is presented to demonstrate the validity of the proposed concept in decision making and a comparison with existing method is provided. The experimental results show that the proposed approach outperforms the existing MADM approaches.

Keywords: Dual hesitant q-rung orthopair fuzzy sets, Dual hesitant q-rung orthopair fuzzy graphs, Hamacher operator, energy of splitting graph, energy of shadow graph, Randić energy

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