Quantile-induced uncertain heavy ordered weighted averaging operator and the application in incentive evaluation problems

To uncertain evaluation problems, we integrate incentive management into the aggregation process and propose an aggregation operator called quantile-induced uncertain heavy ordered weighted averaging (QI-UHOWA) operator, which is an extension of the quantile-induced heavy ordered weighted averaging (QI-HOWA) operator. We provide an approach for determining the quantile order-inducing variables by using the technique for order preference by similarity to ideal solution method and the Hamming distance. In this case, the quantile values are measurements of relative developments of alternatives. Furthermore, we analyze the main properties of the operator including commutativity, boundedness, and monotonicity with uniform development space. The QI-UHOWA weighting vector is calculated using the maximum entropy measure with a given level of incentive attitude. We further expand the weighting method to the case of hierarchical stimulation. Moreover, the QI-UHOWA operator is generalized using the quasi-arithmetic mean. Finally, a numerical example regarding the selection of the optimal candidate(s) is given. The aggregation results are compared with those of the UOWA and QI-UOWA operator to illustrate the validity of the QI-UHOWA operator.