Non-transitive fuzzy dependencies (I)

Abstract

In this work we deal with the problem of defining projection and join operators in a fuzzy database, so that they allow us to compress the information given in a relation r of such a database. Such a compression is possible when a relation satisfies one kind of fuzzy functional dependency (f.f.d.). Such projection and join operators allow us to decompose the original relation r into two new relations in such a way that the amount of information to store is less than originally with r. In this process of decomposition there are two main properties to be achieved. On the one hand, we must be able to test the fuzzy dependency just by looking at one of the projections: as it has less records than r, this represents a computational advantage. On the other hand, the join of both projections is such that we can recover the information we had in r, but with fuzzier values: in order to measure the degree of increasing fuzziness, the concept of granularity level is used. The definition of fuzzy dependency does not verify the transitivity inference axiom.