Algebraic Methods in General Rough Sets

1. Auflage 2018
ISBN: 978-3-030-01161-1
Verlag: Springer International Publishing

Buch, Englisch, 733 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1279 g

Reihe: Trends in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Mani, A.

Düntsch, Ivo

Cattaneo, Gianpiero

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Fuzzy-Set-Theorie

Inhaltsverzeichnis

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