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nth Power Root Fuzzy Sets and Its Topology
Tareq M. Al-shami,ariwan Z. Ibrahim,Abdelwaheb Mhemdi,Radwan Abu-Gdairi 한국지능시스템학회 2022 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.22 No.4
One of the most useful expansions of fuzzy sets for coping with information uncertaintiesis the q-rung orthopair fuzzy sets. In such circumstances, in this article, we define a novelextension of fuzzy sets called nth power root fuzzy set (briefly, nPR-fuzzy set) and elucidatetheir relationship with intuitionistic fuzzy sets, SR-fuzzy sets, CR-fuzzy sets and q-rungorthopair fuzzy sets. Then, we provide the necessary set of operations for nPR-fuzzy sets aswell as study their various features. Furthermore, we familiarize the concept of nPR-fuzzytopology and investigate the basic aspects of this topology. In addition, we define separatednPR-fuzzy sets and then present the concept of disconnected nPR-fuzzy sets. Moreover, westudy and characterize nPR-fuzzy continuous maps in great depth. Finally, we establish T0and T1 in nPR-fuzzy topologies and discover the links between them.