ISBN:
9781402061646
Language:
English
Pages:
Online-Ressource
,
v.: digital
Edition:
Online-Ausg. Springer eBook Collection. Humanities, Social Science and Law Electronic reproduction; Available via World Wide Web
Series Statement:
Trends in Logic 25
Keywords:
Logic
;
Philosophy (General)
;
Fuzzy-Logik
;
Fuzzy-Logik
Abstract:
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.
Abstract:
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.
Description / Table of Contents:
Front Matter; Sets, Relations, And Functions; Lattices; L-Fuzzy Relations; Categories Of Relations; Categories Of L-Fuzzy Relations; Fuzzy Controllers In Goguen Categories; Back Matter
Note:
Includes bibliographical references and index
,
Electronic reproduction; Available via World Wide Web
DOI:
10.1007/978-1-4020-6164-6
URL:
Volltext
(lizenzpflichtig)
