On sets of graded attribute implications with witnessed non-redundancy.

We study properties of particular non-redundant sets of if-then rules describing dependencies between graded attributes. The semantics of the considered rules is parameterized by linguistic hedges. In the setting of general idempotent truth-stressing hedges, we introduce notions of saturation and witnessed non-redundancy of sets of graded attribute implications. Furthermore, we 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. For the special case of graded attribute implications parameterized by globalization, we introduce an algorithm which transforms any complete set of if-then rules into a base given by pseudo-intents. Experimental evaluation is provided to compare the method of obtaining bases with earlier graph-based approaches.