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.

Texte du rabat

In 1982, Professor Pawlak published his seminal paper on what he called "rough sets" - a work which opened a new direction in the development of theories of incomplete information. Today, a decade and a half later, the theory of rough sets has evolved into a far-reaching methodology for dealing with a wide variety of issues centering on incompleteness and imprecision of information - issues which playa key role in the conception and design of intelligent information systems. "Incomplete Information: Rough Set Analysis" - or RSA for short - presents an up-to-date and highly authoritative account of the current status of the basic theory, its many extensions and wide-ranging applications. Edited by Professor Ewa Orlowska, one of the leading contributors to the theory of rough sets, RSA is a collection of nineteen well-integrated chapters authored by experts in rough set theory and related fields. A common thread that runs through these chapters ties the concept of incompleteness of information to those of indiscernibility and similarity.

Contenu

Introduction: What You Always Wanted to Know about Rough Sets.- Rough Sets and Decision Rules: Synthesis of Decision Rules for Object Classification; On the Lower Boundaries in Learning Rules from Examples; On the Best Search Method in the LEM1 and LEM2 Algorithms.- Algebraic Structure of Rough Set Systems: Rough Sets and Algebras of Relations; Rough Set Theory and Logic-Algebraic Structures.- Dependence Spaces: Dependence Spaces of Information Systems; Applications of Dependence Spaces.- Reasoning About Constraints: Indiscernibility-Based Formalization of Dependencies in Information Systems; Dependencies between Many-Valued Attributes.- Indiscernibility-Based Reasoning: Logical Analysis of Indiscernibility; Some Philosophical Aspects of Indiscernibility; Rough Mereology and Anayltical Morphology.- Similarity-Based Reasoning: Similarity Versus Preference in Fuzzy-Based Logics; A Logic for Reasoning about Similarity; Information Systems, Similarity Relations and Modal Logics.- Extended Rough Set-Based Deduction Methods: Axiomatization of Logics Based on Kripke Models with Relative Accessibility Relations; Rough Logics: A Survey with Further Directions; On the Logic with Rough Quantifier.