ENGLISH

Goguen Categories: A Categorical Approach to L-fuzzy Relations

By Michael Winter

Book information

Publisher
Springer
Year
2007
ISBN
9789048175543, 1402061633, 9781402061646, 9781402061639, 9048175542
DOI
10.1007/978-1-4020-6164-6
Language
english
Format
PDF
Filesize
3 MB (3094890 bytes)
Series
Trends in Logic 25
Pages
217\217
Topic
Mathematics Logic
Orientation
portrait
Paginated
yes
Scanned
no
Time added
2011-06-04 13:46:07
Logic

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.

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