  In 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
non-redundant set of graded attribute implications with saturated consequents
whose non-redundancy 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.
