(Type-M Functional Dependency): Let R be a relation with attribute set U, and X, Y ? U. Xg1(t’) ? Yg2(t’’) is a type-M functional dependency (MFD) relation if and only if for any two tuples t1 and t2 in R that have t1[X] ?g1(t’) t2[X], then t1[Y] ?g2(t’’) t2[Y], where g1?TD(X) and g2?TD(Y), whereas t’ and t’’ ? [0,1] are thresholds.
Published in Chapter:
Imprecise Functional Dependencies
Vincenzo Deufemia (Università di Salerno, Italy), Giuseppe Polese (Università di Salerno, Italy), and Mario Vacca (Università di Salerno, Italy)
Copyright: © 2009
|Pages: 9
DOI: 10.4018/978-1-60566-242-8.ch022
Abstract
Functional dependencies represent a fundamental concept in the design of a database since they are capable of capturing some semantics of the data strongly connected with the occurrence of redundancy in a database. The development of applications working on fuzzy and multimedia databases has required the extension of the functional dependency notion to these new types of data. Unfortunately, the concept of imprecise functional dependence or fuzzy functional dependence (IFD, for short) has not had a cogent and largely accepted definition yet. In fact, in attempt to capture different aspects of this notion of many proposals of IFD definition exist in literature, all having semantics and objectives somewhat unclear, especially with respect to the concern of redundancy (Bosc, et al., 1994, Cubero & Vila, 1994, Raju & Majumdar, 1988, Tyagi, et al., 2005, Wang, et al., 2000). Moreover, the debate on the definition of the concept of fuzzy functional dependency seems to be still in progress, as shown by the following question: “But the question remains: are these extended notions of functional dependency a natural generalization?” (Tyagi et al., 2005).