Some Operators Based on qth Rung Root Orthopair Fuzzy Sets and Their Application in Multi-criteria Decision Making

Intuitionistic fuzzy sets have been widely studied and applied as an important means of dealing with information uncertainty. However, the existing intuitionistic fuzzy sets and their extension methods are limited and single in their fuzzy spatial representation of information. Under this environment, this paper proposes a new generalized fuzzy set, called qth Rung Root Orthopair Fuzzy Sets (q-RROFS). Since the q-RROFS can adjust the range of fuzzy space expression by the parameter q, it is superior to intuitionistic fuzzy sets, SR-fuzzy sets, and CR-fuzzy sets. We give some definitions and properties of q-RROFS and give their proofs. Under the q-RROFS, we give its operations and properties and introduce four new weighted aggregation operators, namely, qth Rung Root Orthopair Fuzzy-weighted average operator (q-RROFWA), qth Rung Root Orthopair Fuzzy-weighted geometric operator (q-RROFWG), qth Rung Root Orthopair Fuzzy-weighted power average operator (q-RROFWPA), and qth Rung Root Orthopair Fuzzy-weighted power geometric operator (q-RROFWPG). We discuss the properties of these operators in detail and follow the proof procedure. Then, we give a Multi-criteria decision-making approach under q-RROFS. Finally, we illustrate the effectiveness and applicability of the proposed methodology through practical application examples and comparisons with other methods.