Data Summarization in Relational Databases Through FuzzyDependenciesJ

In this paper we deal with the problem of data summarization through the concept of fuzzy dependency. We introduce a projection operator which leads us to partition a database into two projections with a less amount of information. Thus, we can replace the original relation by those projections. In this process we must guarantee that we can recover the original relation, through the projections, using a special join operator. This process can be done whenever the relation satisses a fuzzy dependency. The projection represents a set of fuzzy rules explaining such a dependency. Also, we show that this deenition of dependency maintains the good properties of completeness as in the classical case. 1 Preliminaries 1.1 Introduction The treatment of non crisp information in databases has been accomplished over the last decade by several authors. The study of incomplete information has been addressed in 16, 17, 18, 21], and the study of uncertain in object data models has been accomplished in 25, 29, 33]. Logic and imprecise information have been studied in 15, 22, 30], whereas fuzzy 32] data models have been introduced in 3, 23, 27]. In this work we deal with the problem of treatment of fuzzy dependencies 9, 12, 4, 23, 24, 31] in fuzzy and non fuzzy (crisp) relational databases. We introduce a generalization of the process of normalization, which leads us to compress the original data appearing in a table of a relational database. This allows us to discover dependencies between attributes in a relation r not detected by classical functional dependencies, and furthermore, decompose r into two new relations called, r 1 and r 2 in such a way that: { r 2 stores the information given in the fuzzy dependency, whereas r 1 represents the other information appearing in r. For new entries to the database, we can test the fuzzy dependency just by looking at the tuples in r 2. { The amount of information stored in r 1 and in r 2 is less than in r. { The original data appearing in r can be recovered (in fuzzy terms) through a fuzzy join of r 1 and r 2. The organization of the work is as follows: in this section we overview basic elements of the relational database model and introduce the notion of resemblance relation which will be used to relax the concept of functional dependency; we also give the …