Generalized Aggregation Operator and Its Application to Clustering

Abstract

While AO have been discussed as an operator for scalars but have not been discussed in a vector space, even though, a lot of data analyses treat data as vectors. We propose generalized aggregation operators (GAO) extended from aggregation operators (AO) to operators based on vectors. We apply GAO to a kernel fuzzy clustering model. Conventionally, the model uses an inner product to represent the common property; however, the real world data has variability for the common property. This means that we can not always capture the common property of objects by using the inner product. Several numerical examples show better performance for the application of GEO to the kernel fuzzy clustering model.