Abstract
We present a new method based on the use of fuzzy transforms for detecting coarse-grained association rules in the datasets. The fuzzy association rules are represented in the form of linguistic expressions and we introduce a pre-processing phase to determine the optimal fuzzy partition of the domains of the quantitative attributes. In the extraction of the fuzzy association rules we use the AprioriGen algorithm and a confidence index calculated via the inverse fuzzy transform. Our method is applied to datasets of the 2001 census database of the district of Naples (Italy); the results show that the extracted fuzzy association rules provide a correct coarse-grained view of the data association rule set.
Highlights
Fuzzy association rules extraction [1] is a fundamental process in data mining for many topics as classification and information retrieval
The fuzzy association rules are represented in the form of linguistic expressions and we introduce a pre-processing phase to determine the optimal fuzzy partition of the domains of the quantitative attributes
In this paper we follow this approach; our framework is composed from a pre-processing phase, and of two successive processes for extracting the fuzzy association rules
Summary
Fuzzy association rules extraction [1] is a fundamental process in data mining for many topics as classification and information retrieval. The method given in [31] can be very useful when we need to extract fuzzy association rules in an approximate way from a dataset; for each attribute a coarse-grained uniform fuzzy partition of its context is created and the evaluative linguistic expression in the consequent represents a weighted mean of the values of the attribute Xz. as pointed in [35], this approach does not take into account the necessity to have the data sufficiently dense with respect to the chosen fuzzy partition, otherwise the F-transforms cannot be used. Theorems 1 and 2 assure that a discrete (even multi-dimensional) function can be approximated arbitrarily with a suitable inverse (multidimensional) F. transform provided that a convenient fuzzy partition of the universe of discourse is found via related basic functions. We assume several values of n (resp., n(1), . . . , n(k)) testing that the set P is sufficiently dense with respect to the related fuzzy partition (resp., partitions) and we use the two indexes (6) and (7) for controlling the choice of the best fuzzy partition (resp., partitions)
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