Algebraic Methods in General Rough Sets

A. Mani, Gianpiero Cattaneo, Ivo Düntsch (Herausgeber)

Buch | Hardcover

XVI, 733 Seiten

2019
Springer International Publishing (Verlag)
978-3-030-01161-1 (ISBN)

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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.

Introduction.- Algebraic Methods for Rough Approximation Spaces by Lattice Interior-Closure 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

Erscheinungsdatum	25.01.2019
Reihe/Serie	Trends in Mathematics
Zusatzinfo	XVI, 733 p. 120 illus., 4 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1286 g
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	algebras of rough sets • BZMV-algebras • double stone algebras • granular operator spaces • granular rough sets • ideal-based rough sets • Inverse Problems • Kleene algebras • knowledge algebras • lukasiewicz algebras • nelson algebras • ortho-pairs • proto-vague semantics • quasi- varieties • rough dualities • rough orders • rough rings • rough semigroups • rough Y-systems • s-Approximation spaces
ISBN-10	3-030-01161-5 / 3030011615
ISBN-13	978-3-030-01161-1 / 9783030011611
Zustand	Neuware