Goguen Categories

A Categorical Approach to L-fuzzy Relations

By:

Michael Winter

Format:

Paperback / softback

Series:

Trends in Logic

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Description

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.

Release date Australia

November 30th, 2010

Author

Michael Winter

Series

Trends in Logic

Pages

208

Edition

Softcover reprint of hardcover 1st ed. 2007

Audience

Professional & Vocational

Illustrations

XII, 208 p.

Dimensions

156x234x11

ISBN-13

9789048175543

Product ID

11081874

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