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Extra info for Computing Particle Properties
B) The second normal form (2NF): R is in 2NF, denoted by R e 2NF, if and only if R e INF and for any non-prime attribute A, K ->/A. (c) The third normal form (3NF): R is in 3NF, denoted by R e 3NF, if and only if R e INF and for any X —» A (A ctX), either X is a superkey of R or A is a set of prime attributes. (d) The Boyce-Codd normal form (BCNF): R is in BCNF, denoted by R e BCNF, if and only if Re INF and for any X - » A (A dX), either X is a superkey of R. A lower NF can be normalized into a higher NF through relation schema decomposition (via projection).
2. 3 Fuzzy Sets in Database Modeling A large number of data models have been proposed to handle uncertainty and vagueness. Most of these models are based on the same paradigms. Vagueness and uncertainty are generally modeled with fuzzy sets and possibility theory (Zadeh, 1965 & 1978). Many of the existing approaches dealing with imprecision and uncertainty are based on the theory of fuzzy sets. Fuzzy information has been extensively investigated in the context of the relational model (Petry, 1996; Chen, 1999).
In the relational databases, functional dependencies can be defined as follows. 24 Chapter 2 Definition: For a relation r (R), in which R denotes the schema, its attribute set is denoted by £/, and I , 7 c f/? we say r satisfies the functional dependency FD: X-> 7, if (\/t e r) (\/s er)(t[X\=s[X\=>t[Y]=s ). Based on the concept of functional dependency, the partial/full functional dependencies and the transitive functional dependency can be defined as follows. Definition: For a relation r (R), in which R denotes the schema, its attribute set is denoted by U, and I , 7 c (7, we say 7 i s fully functionally dependent on J 5 denoted byX—»/ 7, if and only ifX-^ 7 and there does not exit X a X (X * O) such that X9 -> 7.