On attribute reduction in concept lattices: Methods based on discernibility matrix are outperformed by basic clarification and reduction

Using Covering Reduction to Identify Reducts for Object-Oriented Concept Lattices

An object-oriented concept lattice, as an important generalization of classic concept lattices, is a bridge between formal concept analysis and rough set theory. This paper presents an application of covering reduction in formal concept analysis. It studies attribute reduction, object reduction, and bireduction for object-oriented concept lattices. We show that attribute and object reductions for object-oriented concept lattices are equivalent to covering reductions. Using a Boolean matrix transformation, we derive the corresponding algorithms to identify all reducts. In contrast to existing discernibility matrix-based reduction algorithms for object-oriented concept lattices, our algorithms omit the calculation of concept lattices, discernibility matrices, and discernibility functions. The algorithms save substantial time and are a significant improvement over discernibility matrix-based techniques.

Characterizing One-Sided Formal Concept Analysis by Multi-Adjoint Concept Lattices

Managing and extracting information from databases is one of the main goals in several fields, as in Formal Concept Analysis (FCA). One-sided concept lattices and multi-adjoint concept lattices are two frameworks in FCA that have been developed in parallel. This paper shows that one-sided concept lattices are particular cases of multi-adjoint concept lattices. As a first consequence of this characterization, a new attribute reduction mechanism has been introduced in the one-side framework.

The Reduct of a Fuzzy $$\beta $$-Covering

This paper points some mistakes of three algorithms of updating the reduct in fuzzy \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}-covering via matrix approaches while adding and deleting some objects of the universe, and gives corrections of these mistakes. Moreover, we study the reduct of a fuzzy \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}-covering while adding and deleting objects further.

Resilience Analysis of Critical Infrastructures: A Cognitive Approach Based on Granular Computing

A great impetus for the study of resilience in critical infrastructures (CIs) is found in the large number of initiatives and international research programmes from U.S., EU, and Asia. Politicians, decision makers, and citizens are now aware of the drastic consequences that can have the cascading effects of an adverse event in these large scale infrastructures. However, the study of resilience in CIs is challenging for several reasons, among which their large scale and interdependencies. We have to consider also that adverse events, e.g., attacks, natural hazards, or man-made disasters, suddenly occur and evolve rapidly, giving us little time to take decisions and react to them. Approximate reasoning and rapid decision making have to be considered requirements for resilience analysis of CIs. The main result presented in this paper relates to a systemic integration of granular computing (GrC) and resilience analysis for CIs. Each phase of our approach presents distinctive aspects but, overall, we argue the merit of this paper consists in the originality of the study, being this the first work that combines GrC and resilience analysis of CIs. This paper reports an illustrative example that shows how to apply our results, and a discussion on the necessary contextualizations and extensions of the GrC results to be better adapted for CIs resilience.