Authors:
- Rigorous application of formal logics to fuzzy concepts
- A mathematical introduction to fuzzy concepts for researchers in formal logics
- Unique approach to formal semantics of fuzzy controllers
Part of the book series: Trends in Logic (TREN, volume 25)
Buy it now
Buying options
Tax calculation will be finalised at checkout
Other ways to access
This is a preview of subscription content, log in via an institution to check for access.
Table of contents (6 chapters)
-
Front Matter
-
Back Matter
About this book
Goguen categories extend the relational calculus and its categorical formalization to the fuzzy world. Starting from the fundamental concepts of sets, binary relations and lattices this book introduces several categorical formulations of an abstract theory of relations such as allegories, Dedekind categories and related structures. It is shown that neither theory is sufficiently rich to describe basic operations on fuzzy relations. The book then introduces Goguen categories and provides a comprehensive study of these structures including their representation theory, and the definability of norm-based operations.
The power of the theory is demonstrated by a comprehensive example. A certain Goguen category is used to specify and to develop a fuzzy controller. Based on its abstract description as well as certain desirable properties and their formal proofs, a verified controller is derived without compromising the - sometimes - intuitive choice of norm-based operations by fuzzy engineers.
Authors and Affiliations
-
Brock University, St. Catharines, Canada
Michael Winter
Bibliographic Information
Book Title: Goguen Categories
Book Subtitle: A Categorical Approach to L-fuzzy Relations
Authors: Michael Winter
Series Title: Trends in Logic
DOI: https://doi.org/10.1007/978-1-4020-6164-6
Publisher: Springer Dordrecht
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media B.V. 2007
Hardcover ISBN: 978-1-4020-6163-9Published: 24 July 2007
Softcover ISBN: 978-90-481-7554-3Published: 30 November 2010
eBook ISBN: 978-1-4020-6164-6Published: 14 August 2007
Series ISSN: 1572-6126
Series E-ISSN: 2212-7313
Edition Number: 1
Number of Pages: XII, 208
Topics: Logic