Scaled Prioritized Geometric Aggregation Operators and Their Applications to Decision Making

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This paper uses the priority labels to express the detailed prioritized relationship between criteria and develops some scaled prioritized geometric aggregation operators, including the scaled prioritized geometric score (SPGS) operator and the scaled prioritized geometric averaging (SPGA) operator. We also present the uncertain scaled prioritized geometric scoring (USPGS) operator and the uncertain scaled prioritized geometric averaging (USPGA) 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. The principal advantage of these scaled prioritized geometric aggregation operators is that they are very stable and satisfy monotonicity. Furthermore, we investigate approaches to multi-attribute decision making based on the proposed operators or models and examples are illustrated to show the feasibility and validity of the new approaches. Finally, some further discussions are given.