On the properties of the generalized OWHA operators and their application to group decision making

Harmonic mean is suitable to aggregate negative indicators. In order to improve the flexibility of harmonic mean for modeling many situations, the ordered weighted harmonic averaging (OWHA) operator is extended to provide a new class of operators called the generalized OWHA (GOWHA) operators, and investigate some desirable properties of them. When different parameter of the GOWHA operator is employed, various conventional aggregation operators can be deduced, such as the ordered weighted averaging (OWA) operator and the ordered weighted geometric averaging (OWGA) operator. We further demonstrate that the OWHA operator and the GOWHA operator exhibit monotonicity with respect to the weighting vector. Furthermore, we introduce the generalized hybrid harmonic averaging (GHHA) operator, which can reflect the importance degrees of both the given arguments and the ordered position of the arguments. Finally, a new approach on the basis of the GHHA operator is presented in an example of an investment project with group decision making.