Computing sets of graded attribute implications with witnessed non-redundancy

Abstract

a b s t r a c tIn this paper we extend our previous results on sets of graded attribute implications with witnessed non-redundancy. We assume finite residuated lattices as structures of truth degrees and use arbitrary idempotent truth-stressing linguistic hedges as parameters which influence the semantics of graded attribute implications. In this setting, we introduce algorithm which transforms any set of graded attribute implications into an equivalent nonredundant set of graded attribute implications with saturated consequents whose nonredundancy is witnessed by antecedents of the formulas. As a consequence, we solve the open problem regarding the existence of general systems of pseudo-intents which appear in formal concept analysis of object-attribute data with graded attributes and linguistic hedges. Furthermore, we show a polynomial-time procedure for determining bases given by general systems of pseudo-intents from sets of graded attribute implications which are complete in data.

Impact of Local Congruences in Attribute Reduction

“…From the previous examples, we deduce that when the induced equivalence relation does not provide convex sublattices as equivalence classes, the use of local congruence relations alters the original attribute reduction, increasing the number of attributes to be removed. Moreover, it would be interesting to highlight these attributes, record its relationship with the removed attributes and the impact in attribute implications [4,5,9,19].…”