Scaled prioritized aggregation operators and their applications to decision making

As an extension of the prioritized aggregation operators by Yager (Int J Approx Reason 48:263–274, 2008), this paper uses the priority labels to express the prioritized relationship between criteria and presents some scaled prioritized aggregation operators, including the scaled prioritized score operator and the scaled prioritized averaging operator. Moreover, we consider the priority under uncertain environment and develop the uncertain prioritized aggregation operators, including the uncertain prioritized scoring operator and the uncertain prioritized averaging operator. We investigate the properties of these operators and build the models to derive the weights by maximizing square deviations from a possible range to distinguish the candidate alternatives mostly. Furthermore, approaches to multi-attribute decision making based on the proposed operators are given, which have benefits over the TOPSIS method (Behzadian, Expert Syst Appl 39:13051–13069, 2012) and the methods based on the OWA operator (Zhou and Chen, Fuzzy Sets Syst 168:18–34, 2011) when prioritized relationship between criteria is considered. Finally, examples are illustrated to show the feasibility and validity of the new approaches to the application of decision making.