Data mining using L-fuzzy concept analysis.
Association rules in data mining are implications between attributes of objects that hold in all instances of the given data. These rules are very useful to determine the properties of the data such as essential features of products that determine the purchase decisions of customers. Normally the data is given as binary (or crisp) tables relating objects with their attributes by yes-no entries. We propose a relational theory for generating attribute implications from many-valued contexts, i.e, where the relationship between objects and attributes is given by a range of degrees from no to yes. This degree is usually taken from a suitable lattice where the smallest element corresponds to the classical no and the greatest element corresponds to the classical yes. Previous related work handled many-valued contexts by transforming the context by scaling or by choosing a minimal degree of membership to a crisp (yes-no) context. Then the standard methods of formal concept analysis were applied to this crisp context. In our proposal, we will handle a many-valued context as is, i.e., without transforming it into a crisp one. The advantage of this approach is that we work with the original data without performing a transformation step which modifies the data in advance.
data mining, formal concept analysis, fuzzy formal concept analysis, attribute implication, relational algebra
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