Computing sets of graded attribute implications with witnessed non-redundancy
This work addresses incremental improvements in formal concept analysis for researchers dealing with object-attribute data with graded attributes and linguistic hedges.
The paper tackles the problem of transforming sets of graded attribute implications into equivalent non-redundant sets with witnessed non-redundancy, using finite residuated lattices and idempotent truth-stressing linguistic hedges, and solves an open problem regarding general systems of pseudo-intents in formal concept analysis with graded attributes and hedges.
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.