Computing sets of graded attribute implications with witnessed non-redundancy

TL;DR

This paper develops an algorithm for transforming sets of graded attribute implications into non-redundant, equivalent sets with witnessed non-redundancy, addressing an open problem in formal concept analysis with graded attributes.

Contribution

It introduces a polynomial-time procedure for constructing bases from complete sets of graded attribute implications, solving a key open problem.

Findings

Algorithm transforms any set into a non-redundant equivalent set

Addresses the existence of pseudo-intents in graded formal concept analysis

Provides polynomial-time method for basis determination

Abstract

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.