Improved VIKOR methodology based on $q$-rung orthopair hesitant fuzzy rough aggregation information: application in multi expert decision making

The main objective of this article is to introduce the idea of a q-rung orthopair hesitant fuzzy rough set (q-ROHFRS) as a robust fusion of the q-rung orthopair fuzzy set, hesitant fuzzy set, and rough set. A q-ROHFRS is a novel approach to uncertainty modelling in multi-criteria decision making (MCDM). Various key properties of q-ROHFRS and some elementary operations on q-ROHFRSs are proposed. Based on the q-ROHFRS operational laws, novel q-rung orthopair hesitant fuzzy rough weighted averaging operators have been developed. Some interesting properties of the proposed operators are also demonstrated. Furthermore, by using the proposed aggregation operator, we develop a modified VIKOR method in the context of q-ROHFRS. The outcome of this research is to rank and select the best alternative with the help of the modified VIKOR method based on aggregation operators for q-ROHFRS. A decision-making algorithm based on aggregation operators and extended VIKOR methodology has been developed to deal with the uncertainty and incompleteness of real-world decision-making. Finally, a numerical illustration of agriculture farming is considered to demonstrate the applicability of the proposed methodology. Also, a comparative study is presented to demonstrate the validity and effectiveness of the proposed approach. The results show that the proposed decision-making methodology is feasible, applicable, and effective to address uncertainty in decision making problems.