in the first row (i.e. attribute A1) and the second column (i.e., attribute A2). The positions of 0 in row 1 indicate that A1 is neither directly connected to itself nor to attributes A3 and A5 to A9. The direct and indirect relationships among attributes are specified by the binary reachability matrix (R) of order (k,k), where k is the number of attributes. To obtain the R matrix from the A matrix, Boolean addition and multiplication operations are performed on the adjacency matrix, meaning where n is the integer required to reach invariance, , and I is the identity matrix. The R matrix for the Ratio and Algebra hierarchy is shown next. Similar to the A matrix, each row and column in the matrix represents one attribute; the first row and column represents attribute A1 and the last row and column represents attribute A9. The first attribute is either directly or indirectly connected to all attributes A1 to A9. This is represented by the presence of 1's in all columns of row 1 (i.e., representing attribute A1). In the R matrix, an attribute is considered related to itself resulting in 1's along the main diagonal. Referring back to the hierarchy, it is shown that attribute A1 is directly connected to attribute A2 and indirectly to A3 through its connection with A2. Attribute A1 is indirectly connected to attributes A5 to A9 through its connection with A4. The potential pool of items is represented by the incidence matrix (Q) matrix of order (k, p), where k is the number of attributes and p is number of potential items. This pool of items represents all combinations of the attributes when the attributes are independent of each other. However, this pool of items can be reduced to form the reduced incidence matrix (Qr), by imposing the constraints of the attribute hierarchy as defined by the R matrix. The Qr matrix represents items that capture the dependencies among the attributes defined in the attribute hierarchy. The Qr matrix is formed using Boolean inclusion by determining which columns of the R matrix are logically included in each column of the Q matrix. The Qr matrix is of order (k,) where k is the number of attributes and i is the reduced number of items resulting from the constraints in the hierarchy. For the Ratio and Algebra hierarchy, the Qr matrix is shown next. The Qr