1 Introduction: What You Always Wanted to Know about Rough Sets.- I Rough Sets and Decision Rules.- 2 Synthesis of Decision Rules for Object Classification.- 3 On the Lower Boundaries in Learning Rules from Examples.- 4 On the Best Search Method in the LEM1 and LEM2 Algorithms.- II Algebraic Structure of Rough Set Systems.- 5 Rough Sets and Algebras of Relations.- 6 Rough Set Theory and Logic Algebraic Structures.- III Dependence Spaces.- 7 Dependence Spaces of Information Systems.- 8 Applications of Dependence Spaces.- IV Reasoning about Constraints.- 9 Indiscernibility-Based Formalization of Dependencies in Information Systems.- 10 Dependencies between Many-Valued Attributes.- V Indiscernibility-Based Reasoning.- 11 Logical Analysis of Indiscernibility.- 12 Some Philosophical Aspects of Indiscernibility.- 13 Rough Mereology and Analytical Morphology.- VI Similarity-Based Reasoning.- 14 Similarity versus Preference in Fuzzy Set-Based Logics.- 15 A Logic for Reasoning about Similarity.- 16 Information Systems, Similarity Relations and Modal Logics.- VII Extended Rough Set-Based Deduction Methods.- 17 Axiomatization of Logics Based on Kripke Models with Relative Accessibility Relations.- 18 Rough Logics: A Survey with Further Directions.- 19 On the Logic with Rough Quantifier.

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.

An up-to-date and highly authoritative account of the current status of the basic theory, extensions and applications of rough sets A must reading for anyone who has a serious interest in information processing and knowledge-based systems

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