The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, from logical and mathematical foundations, through all aspects of rough set theory and its applications, such as data mining, knowledge discovery, and intelligent information processing, to relations between rough sets and other approaches to uncertainty, vagueness, and incompleteness, such as fuzzy sets and theory of evidence.
Volume XXII in the series is a continuation of a number of research streams that have grown out of the seminal work of Zdzislaw Pawlak during the first decade of the 21st century.
Author(s): James F. Peters, Andrzej Skowron
Series: Lecture Notes in Computer Science
Publisher: Springer
Year: 2021
Language: English
Pages: 325
City: Cham
Preface
LNCS Transactions on Rough Sets
Errata
Contents
Decision Trees with at Most 19 Vertices for Knowledge Representation
1 Introduction
2 Two Techniques for Decision Tree Construction
2.1 G-19 Technique
2.2 L-19 Technique
3 Results of Experiments
4 Conclusions
References
||-ROSETTA
1 Introduction
1.1 Background
1.2 ROSETTA
1.3 Open-MP
2 Methods
2.1 Parallel Implementation
2.2 Testing Hardware
2.3 Testing Pipeline
2.4 Tests
3 Results
3.1 Comparisons
4 Conclusions
5 Availability
References
Sequences of Refinements of Rough Sets: Logical and Algebraic Aspects
1 Introduction
2 Preliminaries
2.1 Rough Sets and Orthopairs
2.2 Operations Between Orthopairs
2.3 Ordered Structures
3 Sequences of Refinements of Orthopairs
3.1 Refinement Sequences
3.2 Refinement Sequences as Posets
3.3 Some Properties of Refinement Sequences
3.4 Sequences of Refinements of Orthopairs
4 Sequences of Orthopairs as Kleene Algebras
4.1 From a Safe Refinement Sequence to a Kleene Algebra
4.2 From a Complete Refinement Sequence to a Kleene Algebra
4.3 From a Kleene Algebra to a Refinement Sequence
4.4 Representation Theorems
4.5 Operations Between Sequences of Orthopairs
4.6 Application Scenario
5 Modal Logic and Sequences of Orthopairs
5.1 Modal Logic S5 and Rough Sets
5.2 Modal Logic SOn
5.3 Orthopaired Kripke Model and Sequences of Orthopairs
5.4 Epistemic Logic SOn
6 Conclusions and Future Directions
References
A Study of Algebras and Logics of Rough Sets Based on Classical and Generalized Approximation Spaces
1 Introduction
1.1 Basic Notions from Algebras and Logics
1.2 Classical Rough Set Theory
1.3 Algebras and Logics from Classical Rough Set Theory
1.4 Negations as Modal Operators
1.5 Generalized Rough Sets: Definitions and Properties
1.6 Objectives of This Paper
1.7 Convention
2 Kleene Algebras: Boolean and Rough Set Representations
2.1 Boolean Representation of Kleene Algebras
2.2 Rough Set Representation of Kleene Algebras
2.3 Kleene Logic: 3-Valued Semantics
2.4 Rough Set Semantics for LK and the Kleene Algebra 3
3 Perp Semantics of Some Negations in Classical Rough Set-Theoretic Structures
3.1 Semantics in Kite of Negations
3.2 Semantics in Dual Kite of Negations
3.3 Semantics in United Kite of Negations
4 Discrete Dualities for Kleene, Stone, Double Stone and Regular double Stone Algebras
4.1 Dualities Arising from Compatibility Frames
4.2 Dualities Arising from Exhaustive Frames
4.3 Dualities Arising from K- Frames
5 Granule-Based Rough Sets from Quasi Order-Generated Covering-Based Approximation Spaces, Algebras and Representations
5.1 Granule-Based Definition of Rough Sets in QOCAS
5.2 Classical Algebraic Structures Represented Through the Collection of Definable Sets in QOCAS
5.3 The Collections R and RS of Rough Sets in a QOCAS: Relationships
5.4 Algebraic Structures of R and RS
5.5 Connections with Dominance-Based Rough Set Approach
6 Negations and Logics of Rough Sets from QOCAS
6.1 R and RS with Operators
6.2 Logics of Rough Sets from QOCAS
6.3 New Negations from Pseudo Negation
7 Conclusions and Future Work
7.1 Summary and Conclusions
7.2 Future Work
References
Similarity-based Rough Sets and Its Applications in Data Mining
1 Introduction
2 Theoretical Background
3 Similarity-based Rough Sets
4 Correlation Clustering
5 Comparison Between Covering Based on a Tolerance Relation and Similarity-based Rough Sets
6 Search Algorithms
6.1 Results
7 Similarity-based Rough Sets with Annotation
7.1 Annotation with Random Points
8 Tools of the Annotation
8.1 Visualization of Tolerance Relations
8.2 Representative Members
8.3 First Method
8.4 Second Method – Ranking Algorithm
8.5 Selecting the Representatives
9 Approximation Pairs Based on Representatives
10 Approximation Pairs Based on Similarity-based Rough Sets
10.1 Set-Based Approximation Pairs
10.2 Properties of Approximation
11 A Novel Area of Application – Graph Approximation on Similarity-based Rough Sets
12 Attribute Reduction with Graph Approximation
13 Summary
References
Author Index
