Indexing Possibilistic Numerical Data: The Interval B$^{+}$-tree Approach

Abstract

When record sets become large, indexing becomes a required technique for speeding up querying. This holds for regular databases, but also for ‘fuzzy’ databases. In this paper we propose a novel indexing technique, supporting the querying of imperfect numerical data. A possibility based relational database setting is considered. Our approach is based on a novel adaptation of a B$^{+}$-tree, which is currently still one of the most efficient indexing techniques for databases. The leaf nodes of a B$^{+}$-tree are enriched with extra data and an extra tree pointer so that interval data can be stored and handled with them, hence the name Interval B$^{+}$-tree (IBPT). An IBPT allows to index possibility distributions using a single index structure, offering almost the same benefits as a B$^{+}$-tree. We illustrate how an IBPT index can be used to index fuzzy sets and demonstrate its benefits for supporting ‘fuzzy’ querying of ‘fuzzy’ databases. More specifically, we focus on the handling of elementary query criteria that use the so-called compatibility operator IS, which checks whether stored imperfect data are compatible with user preferences (or not).