On attribute reduction in concept lattices: Experimental evaluation shows discernibility matrix based methods inefficient

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.

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.

Stability Prediction Model of Roadway Surrounding Rock Based on Concept Lattice Reduction and a Symmetric Alpha Stable Distribution Probability Neural Network

To combat the uncertainty of the multiple factors affecting roadway surrounding rock stability, five initial indexes are selected for reduction according to concept lattice theory: rock quality designation (RQD), uniaxial compressive strength (Rc), the integrity coefficient of rock mass, groundwater seepage, and joint condition. The aim of this study is to compute correlation coefficients among various indexes and verify the effectiveness of lattice reduction. Alpha stable distribution is used to replace the commonly used Gauss distribution in probabilistic neural networks. A prediction model for the stability of roadway surrounding rock is then established based on a concept lattice and improved probabilistic neural network. 100 groups of training sample data are plugged into this model one by one to examine its rationality. The established model is employed for engineering application prediction with ten indiscriminate sample groups from the Jianlinshan mining area of the Daye iron mine, revealing accuracy of up to 90%. This demonstrates that our prediction model based on a concept lattice and improved probabilistic neural network has high reliability and applicability.