Factorizing formal contexts from closures of necessity operators

TL;DR

This paper analyzes a method for factorizing formal contexts using necessity operators, extending classical properties to fuzzy contexts for efficient dataset decomposition.

Contribution

It studies the properties of factorization methods based on necessity operators and extends these concepts to fuzzy contexts for improved dataset analysis.

Findings

Analyzed the properties of factorization methods in formal contexts.

Extended classical factorization properties to fuzzy contexts.

Provided insights into independent subcontext computation in fuzzy data.

Abstract

Factorizing datasets is an interesting process in a multitude of approaches, but many times it is not possible or efficient the computation of a factorization of the dataset. A method to obtain independent subcontexts of a formal context with Boolean data was proposed in~\cite{dubois:2012}, based on the operators used in possibility theory. In this paper, we will analyze this method and study different properties related to the pairs of sets from which a factorization of a formal context arises. We also inspect how the properties given in the classical case can be extended to the fuzzy framework, which is essential to obtain a mechanism that allows the computation of independent subcontexts of a fuzzy context.