Goguen Categories

A Categorical Approach to L-fuzzy Relations

  • Michael¬†Winter
Part of the Trends in Logic book series (TREN, volume 25)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Pages 5-41
  3. Pages 43-54
  4. Back Matter
    Pages 197-206

About this book

Introduction

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.

Keywords

Allegories Categories Computer science Fuzzy relations Goguen Relation algebras proof

Authors and affiliations

  • Michael¬†Winter
    • 1
  1. 1.Brock UniversitySt. CatharinesCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4020-6164-6
  • Copyright Information Springer 2007
  • Publisher Name Springer, Dordrecht
  • eBook Packages Humanities, Social Sciences and Law
  • Print ISBN 978-1-4020-6163-9
  • Online ISBN 978-1-4020-6164-6