Ebook: Incomplete Information: Rough Set Analysis

The book presents rough set formalisms and methods of modeling and handling incomplete information and motivates their applicability to knowledge representation, knowledge discovery and machine learning. The book focuses on providing representational and inference mechanisms for dealing with two particular aspects of incompleteness, namely indiscernibility and similarity. Those manifestations of particular aspects of incompleteness are inherent in any data structure and any cognitive unit. Knowledge discovered from such an information is uncertain in that it can only be asserted with a tolerance. The methods developed in the book are capable of exposing the limits of that tolerance and of making reliable inferences in the environments where complete information is not available. The framework presented in the book is general and unrestrictive, and yet at the same time captures the relevant features of a great variety of the user's data.

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The book presents rough set formalisms and methods of modeling and handling incomplete information and motivates their applicability to knowledge representation, knowledge discovery and machine learning. The book focuses on providing representational and inference mechanisms for dealing with two particular aspects of incompleteness, namely indiscernibility and similarity. Those manifestations of particular aspects of incompleteness are inherent in any data structure and any cognitive unit. Knowledge discovered from such an information is uncertain in that it can only be asserted with a tolerance. The methods developed in the book are capable of exposing the limits of that tolerance and of making reliable inferences in the environments where complete information is not available. The framework presented in the book is general and unrestrictive, and yet at the same time captures the relevant features of a great variety of the user's data.

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The book presents rough set formalisms and methods of modeling and handling incomplete information and motivates their applicability to knowledge representation, knowledge discovery and machine learning. The book focuses on providing representational and inference mechanisms for dealing with two particular aspects of incompleteness, namely indiscernibility and similarity. Those manifestations of particular aspects of incompleteness are inherent in any data structure and any cognitive unit. Knowledge discovered from such an information is uncertain in that it can only be asserted with a tolerance. The methods developed in the book are capable of exposing the limits of that tolerance and of making reliable inferences in the environments where complete information is not available. The framework presented in the book is general and unrestrictive, and yet at the same time captures the relevant features of a great variety of the user's data.
Content:
Front Matter....Pages I-XII
Introduction: What You Always Wanted to Know about Rough Sets....Pages 1-20
Front Matter....Pages 21-21
Synthesis of Decision Rules for Object Classification....Pages 23-57
On the Lower Boundaries in Learning Rules from Examples....Pages 58-74
On the Best Search Method in the LEM1 and LEM2 Algorithms....Pages 75-91
Front Matter....Pages 93-93
Rough Sets and Algebras of Relations....Pages 95-108
Rough Set Theory and Logic-Algebraic Structures....Pages 109-190
Front Matter....Pages 191-191
Dependence Spaces of Information Systems....Pages 193-246
Applications of Dependence Spaces....Pages 247-289
Front Matter....Pages 291-291
Indiscernibility-Based Formalization of Dependencies in Information Systems....Pages 293-315
Dependencies between Many-Valued Attributes....Pages 316-343
Front Matter....Pages 345-345
Logical Analysis of Indiscernibility....Pages 347-380
Some Philosophical Aspects of Indiscernibility....Pages 381-398
Rough Mereology and Analytical Morphology....Pages 399-437
Front Matter....Pages 439-439
Similarity versus Preference in Fuzzy Set-Based Logics....Pages 441-461
A Logic for Reasoning about Similarity....Pages 462-491
Information Systems, Similarity Relations and Modal Logics....Pages 492-550
Front Matter....Pages 551-551
Axiomatization of Logics Based on Kripke Models with Relative Accessibility Relations....Pages 553-578
Rough Logics: A Survey with Further Directions....Pages 579-600
On the Logic with Rough Quantifier....Pages 601-613

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The book presents rough set formalisms and methods of modeling and handling incomplete information and motivates their applicability to knowledge representation, knowledge discovery and machine learning. The book focuses on providing representational and inference mechanisms for dealing with two particular aspects of incompleteness, namely indiscernibility and similarity. Those manifestations of particular aspects of incompleteness are inherent in any data structure and any cognitive unit. Knowledge discovered from such an information is uncertain in that it can only be asserted with a tolerance. The methods developed in the book are capable of exposing the limits of that tolerance and of making reliable inferences in the environments where complete information is not available. The framework presented in the book is general and unrestrictive, and yet at the same time captures the relevant features of a great variety of the user's data.
Content:
Front Matter....Pages I-XII
Introduction: What You Always Wanted to Know about Rough Sets....Pages 1-20
Front Matter....Pages 21-21
Synthesis of Decision Rules for Object Classification....Pages 23-57
On the Lower Boundaries in Learning Rules from Examples....Pages 58-74
On the Best Search Method in the LEM1 and LEM2 Algorithms....Pages 75-91
Front Matter....Pages 93-93
Rough Sets and Algebras of Relations....Pages 95-108
Rough Set Theory and Logic-Algebraic Structures....Pages 109-190
Front Matter....Pages 191-191
Dependence Spaces of Information Systems....Pages 193-246
Applications of Dependence Spaces....Pages 247-289
Front Matter....Pages 291-291
Indiscernibility-Based Formalization of Dependencies in Information Systems....Pages 293-315
Dependencies between Many-Valued Attributes....Pages 316-343
Front Matter....Pages 345-345
Logical Analysis of Indiscernibility....Pages 347-380
Some Philosophical Aspects of Indiscernibility....Pages 381-398
Rough Mereology and Analytical Morphology....Pages 399-437
Front Matter....Pages 439-439
Similarity versus Preference in Fuzzy Set-Based Logics....Pages 441-461
A Logic for Reasoning about Similarity....Pages 462-491
Information Systems, Similarity Relations and Modal Logics....Pages 492-550
Front Matter....Pages 551-551
Axiomatization of Logics Based on Kripke Models with Relative Accessibility Relations....Pages 553-578
Rough Logics: A Survey with Further Directions....Pages 579-600
On the Logic with Rough Quantifier....Pages 601-613
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