Rough Sets

First book on the foundations of rough sets since 10 years. Presents deep theoretical results in the book form for the first time. Over 300 exercises and an extensive bibliography with all relevant works and current research. Self-contained structure providing all relevant information from respective areas of mathematics and logics.

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.

First book on the foundations of rough sets since 10 years Presents deep theoretical results in the book form for the first time Over 300 exercises and an extensive bibliography with all relevant works and current research Self-contained structure providing all relevant information from respective areas of mathematics and logics Includes supplementary material: sn.pub/extras

Inhalt
1 Rough Set Theory: An Introduction.- 2 The Sentential Calculus.- 3 Logical Theory of Approximations.- 4 ManyValued Sentential Calculi.- 5 Propositional Modal Logic.- 6 Set Theory.- 7 Topological Structures.- 8 Algebraic Structures.- 9 Predicate Calculus.- 10 Independence, Approximation.- 11 Topology of Rough Sets.- 12 Algebra and Logic of Rough Sets.- 13 Infinitevalued Logical Calculi.- 14 From Rough to Fuzzy.- List of Symbols.