Algebraic Methods in General Rough Sets

Description

This unique collection of research papers offers a comprehensive and up-to-date guide to algebraic approaches to rough sets and reasoning with vagueness. It bridges important gaps, outlines intriguing future research directions, and connects algebraic approaches to rough sets with those for other forms of approximate reasoning. In addition, the book reworks algebraic approaches to axiomatic granularity. Given its scope, the book offers a valuable resource for researchers and teachers in the areas of rough sets and algebras of rough sets, algebraic logic, non classical logic, fuzzy sets, possibility theory, formal concept analysis, computational learning theory, category theory, and other formal approaches to vagueness and approximate reasoning. Consultants in AI and allied fields will also find the book to be of great practical value. Front Matter ....Pages i-xvi Introduction (A. Mani, Gianpiero Cattaneo, Ivo Düntsch)....Pages 1-11 Algebraic Methods for Rough Approximation Spaces by Lattice Interior–Closure Operations (Gianpiero Cattaneo)....Pages 13-156 Algebraic Methods for Granular Rough Sets (A. Mani)....Pages 157-335 Three Lessons on the Topological and Algebraic Hidden Core of Rough Set Theory (Piero Pagliani)....Pages 337-415 Irredundant Coverings, Tolerances, and Related Algebras (Jouni Järvinen, Sándor Radeleczki)....Pages 417-457 Algebraic Representation, Dualities and Beyond (A. Mani)....Pages 459-552 Algebraic Methods for Orthopairs and Induced Rough Approximation Spaces (Gianpiero Cattaneo, Davide Ciucci)....Pages 553-640 Rough Objects in Monoidal Closed Categories (Patrik Eklund, María-Ángeles Galán-García)....Pages 641-655 Rough Algebraic Structures Corresponding to Ring Theory (Bijan Davvaz)....Pages 657-695 S-Approximation Spaces (Ali Shakiba)....Pages 697-725 Back Matter ....Pages 727-733