Norm-based distance measure of q-rung orthopair fuzzy sets and its application in decision-making

A q-rung orthopair fuzzy (q-ROF) set (q-ROFS) is one of the advanced fuzzy sets capable of processing complex real-world information satisfactorily. q-ROF distance measures are used to indicate the degree of difference between the data conveyed by q-ROFSs. Though numerous distance measures have been proposed in earlier studies, they cannot meet the axioms of distance measure or exist counter-intuitive cases. This study aims to formulate a novel q-ROF distance measure based on matrix norm and a strictly increasing (or decreasing) function. Further, the originated distance measure is shown to fulfill the axiomatic requirements of the distance function. The proposed measure not only meets the axiomatic definition of distance measure but also remedies the counter-intuitive cases. Appropriate experimental configurations are developed to compare the suggested distance measure with existing measures by employing them in several examples. Following the proposed q-ROF distance measures, a new method for dealing with multi-criteria group decision-making (MCGDM) problems in the q-ROF environment is presented. To illustrate the application potentiality of the established method, a numerical example concerning renewable energy source selection is assessed with q-ROF input. Finally, sensitivity and comparative analyses are executed to verify the stability and efficacy of the provided approach.