Algebraic Methods in General Rough Sets

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.

Detailed up-to-date guide to algebraic approaches to general rough sets and formal algebraic approaches to vagueness. Bridges important gaps and connects algebraic approaches to rough sets with those for other forms of approximate reasoning. Researchers, teachers and AI consultants at all levels of maturity will find this book invaluable.

Contenu
Introduction.- Algebraic Methods for Rough Approximation Spaces by Lattice InteriorClosure Operations.- Algebraic Methods for Granular Rough Sets.- Three Lessons on the Topological and Algebraic Hidden Core of Rough Set Theory.- Irredundant Coverings, Tolerances, and Related Algebras.- Algebraic Representation, Dualities and Beyond.-Algebraic Methods for Orthopairs and Induced Rough Approximation Spaces.- Rough Objects in Monoidal Closed Categories.- Rough Algebraic Structures Corresponding to Ring Theory.- S-approximation Spaces.- Index