On sets of graded attribute implications with witnessed non-redundancy
This work addresses a specific problem in formal concept analysis for researchers in data mining and knowledge representation, presenting an incremental improvement over existing methods.
The paper tackles the problem of generating non-redundant sets of graded attribute implications, which describe dependencies between attributes with degrees, by introducing a method to transform complete sets into bases defined by pseudo-intents, with experimental evaluation comparing it to earlier graph-based approaches.
We study properties of particular non-redundant sets of if-then rules describing dependencies between graded attributes. We introduce notions of saturation and witnessed non-redundancy of sets of graded attribute implications are show that bases of graded attribute implications given by systems of pseudo-intents correspond to non-redundant sets of graded attribute implications with saturated consequents where the non-redundancy is witnessed by antecedents of the contained graded attribute implications. We introduce an algorithm which transforms any complete set of graded attribute implications parameterized by globalization into a base given by pseudo-intents. Experimental evaluation is provided to compare the method of obtaining bases for general parameterizations by hedges with earlier graph-based approaches.