The problem of mining multidimensional inter-transactional association rules was recently introduced in [ACM Trans. Inform. Syst. 18(4) (2000) 423; Proc. of the ACM SIGMOD Workshop on Research Issues on Data Mining and Knowledge Discovery, Seattle, Washington, June 1998, p. 12 1].
In order to reduce the number of fuzzy if then rules, the multidimensional space of input variables (instead of the individual input variable) of fuzzy controllers is partitioned into fuzzy sets.
Due to the complex mapping relationship between product attributes and engineering characteristics, as well as the correlations between engineering characteristics and the engineering constraints on a product, a new product following a probabilistic rule of multidimensional scaling may not be in an optimal position in product engineering space.
In this paper, we extend the previous problem definition based on context expansion, and present a more general form of association rules, named generalized multidimensional inter-transactional association rules.
In this approach, the satisfaction of the structural constraints depends on both the identification rules of the multidimensional elements and the design quality of the source schema.
For the multidimensional case, the component number rule generalizes in a straightforward way to m_{i} = Sigma_{[i,i]} + 1. (40).
Since it is difficult to handle performance index and control rule-base under multidimensional space, almost all studies of multivariable SOFLC use a method for decomposing an n-input/ m-output system into a set of 2-input/1-output systems [ 6, 30, 51].
Indeed [23], proposes a multidimensional analysis approach to define the analysis rules and to help analysts to change the values of given dimensions in order to improve the fact table.
And still the multidimensional quarterback remains the exception, not the rule.
