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4211 Relational Algebra Basic Operators Basic operators of RA are SL, PJ, UN, SD, and CP In the following subsections, we brie y describe these operators Select Operator in Relational Algebra The select operator returns all tuples of the relation whose attribute(s) satisfy the given predicates (conditions) If no condition is speci ed, the select operator returns all tuples of the relation For example, SLbal=1200 (Account) returns all accounts that have a balance of $1200 The result is a relation with four attributes (since the Account relation has four attributes) and as many rows as the number of accounts with a balance of exactly $1200 The predicate bal = 1200 is a simple predicate We can use AND, OR, and NOT to combine simple predicates, making complex predicates.

where FS and FT are fuzzy proximity relations. FS and FT are symmetric and re exive. In fact, the constraint (3.10) expresses that when St1 and St2 are close, then y1 and y2 should be at least as close as them. Moreover, if FT is de ned such that FT y1 ; y2 1 , y1 y2 , the classical functional dependency St1 St2 ) y1 y2 is a consequence of constraint (3.10) using the re exivity of FS. In this case, constraint (3.10) is then clearly stronger than a classical functional dependency. Let St; y 2 M, and St0 ; y0 be the current situation; then we have FS St; St0 FT y; y0

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For example, we can nd the accounts with a balance of $1200 at branch Main using the select expression, SLbal=1200 AND Bname= Main (Account) Project Operator in Relational Algebra The project operator returns the values of all attributes speci ed in the project operation for all tuples of the relation passed as a parameter In a project operation, all rows qualify but only those attributes speci ed are returned For instance, PJ Cname,Ccity (Customer) returns the customer name and the city where the customer lives for each and every customer of the bank Combining Select and Project We can combine the select and project operators in forming complex RA expressions that not only apply a given set of predicates to the tuples of a relation but also trim the attributes to a desired set.

On the German side Friedhelm Hillebrand and Frieder Pernice continued to be the leading technical representatives Proposals from the manufacturers were received in March 1985 After a joint evaluation the Franco-German Working Group recommended to award four contracts, two by DGT and two by the DBP, for the construction of the four demonstrators brie y described in Table 231 DGT was to issue the CD 900 and SFH 900 contracts and the DBP the S 900-D and the MATS-D contracts This raised some problems inside DGT SEL, then still an ITT company was the leader of the CD 900 project but Alcatel was a partner.

For example, assume we want to get the customer ID and customer name for all customers who live in Edina We can do this by combining the SL and the PJ expressions as PJ CID, Cname (SL Ccity= Edina (Customer)) Note that operator precedence is enforced by parentheses In this example, the innermost expression is the SL operation and is carried out rst This expression returns all customers who live in Edina Subsequently, the PJ operator trims the results to only CID and Cname for those customers returned from the SL operation..

Next, taking the rst and second derivatives with respect to the independent variable x will produce the equations YA&B x mA&B YA x mA YB x mB ; YA&B YA YB ; respectively. Information is Additive The information matrix of the combined likelihood function (YA&B in Eq. 7.14) equals the sum of the individual information matrices of the component likelihood functions (YA and YB in Eq. 7.14). Combined Maximum-Likelihood Estimate is a Weighted Average 7.13 evaluated at x 0 is YA&B mA&B YA mA YB mB ; Equation 7:15 7:13 7:14

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