Continuous generalized OWA operator and its application to decision making

Abstract

In this paper we present a new class of operators called the continuous generalized ordered weighted averaging (C-GOWA) operators, which extends the continuous ordered weighted averaging operator. To adapt to uncertain and complex situations in decision making, we use differentiated aggregation method and produce special forms of C-GOWA operator. In addition, we apply the C-GOWA operator to the aggregation of multiple interval arguments and obtain a wide range of aggregation operators. We especially discuss the controlling parameter and the selection of basic unit-interval monotonic function, introduced in the information aggregation, to make it more feasible. We further generalize the previous approaches by using Choquet integral and quasi-arithmetic means, obtaining the combined continuous generalized Choquet integral aggregation operator and the combined continuous quasi-arithmetic Choquet integral aggregation operator. We also present some further extension by using hierarchical aggregation rules, obtaining the ordered hierarchies of the combined C-GOWA operator. Meanwhile, some desirable properties of these operators are investigated. Finally, we give a numerical example to illustrate the application of these operators to group decision making with interval arguments.