Composition of filtering functions

In recent years, due to the increasing popularization of various broadcast services, there has been an increasing demand for information filtering techniques. Although filtering methods that have been proposed filter data in their own ways, mathematical representation of these methods does not exist. Consequently, it is not possible to qualitatively evaluate various filtering methods, to optimize processing methods in filtering, or to design a declarative language for filtering processes. In our previous work we have defined a filtering function that represents filtering as a function, and clarified the properties of different filtering methods. In practice, current filtering methods actually consist of multiple methods. In this paper, we make it possible to qualitatively represent those filtering methods by introducing the concept of composition into the framework of filtering function. Moreover, we reveal the characteristics of those combined filtering methods by clarifying the properties of composite filtering functions.