Attribute Reduction Algorithms Determined by Invariants for Decision Tables

Rough set theory is a field of research pertaining to human-inspired computation. Attribute reduction is an important component of rough set theory and has been extensively studied. The reduction invariant is a key concept for an attribute reduction and finding new reduction invariants is an importa...

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Bibliographic Details
Published in:Cognitive computation Vol. 14; no. 6; pp. 1818 - 1825
Main Author: Liu, Guilong
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2022
Springer Nature B.V
Subjects:
Algorithms
Artificial Intelligence
Boolean
Cognition & reasoning
Computation by Abstract Devices
Computational Biology/Bioinformatics
Computer Science
Decision making
Decision theory
Granular Computing and Three-Way Decisions for Cognitive Analytics
Heuristic
Heuristic methods
Invariants
Mathematical analysis
Matrices (mathematics)
Reduction
Set theory
Invariant
Granular computing
Positive region reduction
Relative reduction
Decision table
ISSN:1866-9956, 1866-9964
Online Access:Get full text
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Summary:Rough set theory is a field of research pertaining to human-inspired computation. Attribute reduction is an important component of rough set theory and has been extensively studied. The reduction invariant is a key concept for an attribute reduction and finding new reduction invariants is an important task of attribute reduction. This paper explores the effect of different reduction invariants on the same attribute reduction types. The aim of this paper was to elucidate the mathematical structure of attribute reduction, thereby facilitating the use of new reduction invariants and their corresponding algorithms for positive region reduction and relative reduction in decision tables. New reduction invariants provide the opportunity to design significantly improved reduction algorithms. Two main reduction algorithms are used to identify reducts. One is a heuristic algorithm and the other is a discernibility matrix-based algorithm. Mathematically, the latter is far more complicated than the former. Although the discernibility matrix-based algorithm has a high time complexity, it remains the only approach to identify all reducts. This paper uses the discernibility matrix-based methods to study the attribute reduction problem. We focus on the mathematical structures of attribute reduction with respect to invariants and provide different algorithms to solve the same reduction problem. This research on reduction invariants provides a new perspective for attribute reduction. Positive region reduction and relative reduction are two frequently used types of reduction for decision tables. We provide three invariants for positive region reduction. Based on these invariants, we derive the corresponding discernibility matrix-based reduction algorithms that yield the same reduction results. For relative reduction, we also obtain similar results regarding invariants and algorithms. The shortcoming of this work is that we do not offer a simpler algorithm than the heuristic algorithm. However, the presented mathematical framework unifies previous work on the subject and is conducive to simplifying the associated decision tables for identifying all of the reducts.
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ISSN:1866-9956
1866-9964
DOI:10.1007/s12559-021-09887-w