Abstract
One of the most useful expansions of fuzzy sets for coping with information uncertainties is the q-rung orthopair fuzzy sets. In such circumstances, in this article, we define a novel extension of fuzzy sets called nth power root fuzzy set (briefly, nPR-fuzzy set) and elucidate their relationship with intuitionistic fuzzy sets, SR-fuzzy sets, CR-fuzzy sets and q-rung orthopair fuzzy sets. Then, we provide the necessary set of operations for nPR-fuzzy sets as well as study their various features. Furthermore, we familiarize the concept of nPR-fuzzy topology and investigate the basic aspects of this topology. In addition, we define separated nPR-fuzzy sets and then present the concept of disconnected nPR-fuzzy sets. Moreover, we study and characterize nPR-fuzzy continuous maps in great depth. Finally, we establish T0 and T1 in nPR-fuzzy topologies and discover the links between them.