This paper converts the transaction database to a

Boolean matrix and deletes the unnecessary rows and columns of the matrix to reduce the scale of the data.

By definition, constraint matrix is a

Boolean matrix and expresses the constraint condition of the constraint system.

PE matrix Q is then defined as an 800 * 90

Boolean matrix. As for a certain fragment of the power demand, the value of each element in its PE matrix is determined as

The

Boolean matrix of [[R.sub.mb]] satisfies {[u.sub.m,b]} = [[R.sub.mb]]{[u.sub.b]}.

This criterion derives from the concept of run used in data compression [28, 33], characterizing the biggest sequences of 1 on a line in a

Boolean matrix. The chosen criterion [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is related to the full number of changes present in the nonordered binary matrix of the same degree of parsimony so that it is not skewed in favour of an infinite parsimony or conversely, of too low a parsimony.

The

Boolean matrix is used to describe the transaction database.

The items are converted into a

Boolean matrix (Tsay & Chiang 2005, Wur & Leu, 1999).

In addition, our method is able to get the last frequent itemsets and generate rules depending on data representation and

Boolean Matrix. This paper is organized in six sections: section 2 reviewed related works, section 3 proposed an automated

Boolean matrix data representation using AVL-Tree, section 4 demonstrated the benefits of data representation, section 5 presented the algorithms, section 6 discussed the experimental results, and section 7 concluded the proposed representation scheme.

Definition 5 (Discrete Jacobian matrix) The discrete Jacobian matrix of f evaluated at point x [member of] [B.sup.n] is the following n x n

Boolean matrixwhere [K.sup.G.sub.DD] is the unassembled global stiffness matrix, B and [B.sup.t] are respectively the

Boolean matrix (transition from the local DOF to the global ones) and its transposed one.

The matrix H is a [n.sub.P] x [n.sub.P]

boolean matrix where [H.sub.i,j] = 1 if paper i contains j in its reference list.