Weak Preservation of Multi-Valued Fusion

Abstract

Fusion functions are important data integration tools that map a multiset of objects (i.e., the sources) onto a single object (i.e., the solution). Traditionally, it is assumed that the objects of interest are single-valued. In this paper, it will be assumed that each object has a multi-valued data structure, leading to a framework of second order fusion functions. An important class of such functions is called preservative and is characterized by the fact that one of the input objects is returned. A disadvantage of these functions is the a-priori limitation of the output space to the input objects. It is investigated here how this disadvantage can be mitigated by studying the principle of weak-preservation. The main idea is hereby that, instead of preserving one of the sources, a characteristic feature of one of the sources is preserved. Three such features will be studied: cardinality, k-cut and multiplicity distribution. It will then be shown how weak-preservation can be utilized in the design of second order fusion functions.