Aggregation of Heterogeneously Related Information with Extended Geometric Bonferroni Mean and Its Application in Group Decision Making

Capturing specific interrelationship among input arguments has great importance in the process of aggregation as they may change the aggregation result significantly, which can lead viable changes in the overall decision outcome. In this study, we attempt to aggregate a set of inputs with certain heterogeneous interrelationship pattern among them. To do this, we introduce a new aggregation operator, which we call the extended geometric Bonferroni mean. We investigate its properties and develop an algorithm to learn its associated parameters based on decision maker's perceived view toward the aggregation process. Moreover, to learn such heterogeneous relationship among the inputs from the data set, we provide a learning algorithm. Examples are given to illustrate the realization of algorithm and to show certain advantages over the existing aggregation operators.