Rough Sets: Mathematical Foundations

Description

A comprehensive introduction to mathematical structures essential for Rough Set Theory. The book enables the reader to systematically study all topics of rough set theory. After a detailed introduction in Part 1 along with an extensive bibliography of current research papers. Part 2 presents a self-contained study that brings together all the relevant information from respective areas of mathematics and logics. Part 3 provides an overall picture of theoretical developments in rough set theory, covering logical, algebraic, and topological methods. Topics covered include: algebraic theory of approximation spaces, logical and set-theoretical approaches to indiscernibility and functional dependence, topological spaces of rough sets. The final part gives a unique view on mutual relations between fuzzy and rough set theories (rough fuzzy and fuzzy rough sets). Over 300 excercises allow the reader to master the topics considered. The book can be used as a textbook and as a reference work. Front Matter....Pages i-xix Front Matter....Pages 1-1 Rough Set Theory: An Introduction....Pages 3-92 Front Matter....Pages 93-93 The Sentential Calculus....Pages 95-120 Logical Theory of Approximations....Pages 121-136 Many—Valued Sentential Calculi....Pages 137-158 Propositional Modal Logic....Pages 159-172 Set Theory....Pages 173-212 Topological Structures....Pages 213-250 Algebraic Structures....Pages 251-272 Predicate Calculus....Pages 273-296 Front Matter....Pages 297-297 Independence, Approximation....Pages 299-330 Topology of Rough Sets....Pages 331-360 Algebra and Logic of Rough Sets....Pages 361-410 Front Matter....Pages 411-411 Infinite—valued Logical Calculi....Pages 413-464 From Rough to Fuzzy....Pages 465-500 Back Matter....Pages 501-534