On sets of graded attribute implications with witnessed non-redundancy

TL;DR

This paper investigates non-redundant sets of graded attribute implications, introducing concepts like saturation and witnessed non-redundancy, and presents an algorithm to generate bases using pseudo-intents, with experimental comparisons to existing methods.

Contribution

It introduces new notions of saturation and witnessed non-redundancy for graded attribute implications and provides an algorithm to construct bases using pseudo-intents.

Findings

The algorithm effectively transforms complete sets into bases with pseudo-intents.

Experimental results compare hedge-based methods with graph-based approaches.

The proposed approach improves understanding of redundancy in graded attribute implications.

Abstract

We study properties of particular non-redundant sets of if-then rules describing dependencies between graded attributes. We introduce notions of saturation and witnessed non-redundancy of sets of graded attribute implications are 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. We introduce an algorithm which transforms any complete set of graded attribute implications parameterized by globalization into a base given by pseudo-intents. Experimental evaluation is provided to compare the method of obtaining bases for general parameterizations by hedges with earlier graph-based approaches.