Description of sup- and inf-preserving aggregation functions via families of clusters in data tables

TL;DR

This paper bridges aggregation functions and formal concept analysis, using Galois connections to characterize sup- and inf-preserving functions, with potential applications in biclustering and data mining.

Contribution

It introduces a novel method linking aggregation functions with formal concept analysis through Galois connections, providing a complete description of these functions.

Findings

Galois connections describe sup- and inf-preserving aggregation functions

The method offers an elegant, complete characterization of these functions

Applications in biclustering and fuzzy FCA are discussed

Abstract

Connection between the theory of aggregation functions and formal concept analysis is discussed and studied, thus filling a gap in the literature by building a bridge between these two theories, one of them living in the world of data fusion, the second one in the area of data mining. We show how Galois connections can be used to describe an important class of aggregation functions preserving suprema, and, by duality, to describe aggregation functions preserving infima. Our discovered method gives an elegant and complete description of these classes. Also possible applications of our results within certain biclustering fuzzy FCA-based methods are discussed.