Generalized exponential multiple averaging operator and its application to group decision making

Abstract

The existing information aggregation operators are always the extensions of the ordered weighted averaging (OWA) operator on weighting form or data type. In this paper, the generalized ordered weighted exponential multiple averaging (GOWEMA) operator is developed based on a minimization problem with penalty function. It unifies the geometric mean and the generalized ordered weighted averaging (GOWA) operator with the generalized ordered weighted harmonic averaging (GOWHA) operator in the same formulation. Then the main properties and families of the new operator are investigated. Moreover, an orness measure of the GOWEMA operator and the generalized lest squares method (GLSM) are presented to determine the GOWEMA operator weights. Finally, we give a numerical example of an investment selection to illustrate the application of the GOWEMA operator to multiple attribute group decision making.