A Relation-Algebraic Theory of Bisimulations
Fundamenta Informaticae
A survey on fuzzy relational equations, part I: classification and solvability
Fuzzy Optimization and Decision Making
Cardinal Addition in Distributive Allegories
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Complements in Distributive Allegories
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Determinisation of relational substitutions in ordered categories with domain
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
Ambiguous representations as fuzzy relations between sets
Fuzzy Sets and Systems
Dedekind categories with cutoff operators
Fuzzy Sets and Systems
Relation algebraic approaches to fuzzy relations
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
A first-order calculus for allegories
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
Constructions around partialities
RAMICS'11 Proceedings of the 12th international conference on Relational and algebraic methods in computer science
A Relation-Algebraic Theory of Bisimulations
Fundamenta Informaticae
Point axioms in dedekind categories
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
Relation algebras, matrices, and multi-valued decision diagrams
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
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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.