Fuzzifying modal algebra

  • Fuzzy relations are mappings from pairs of elements into the interval [0,1]. As a replacement for the complement operation one can use the mapping that sends x to 1-x. Together with the concepts of t-norm and t-conorm a weak form of Boolean algebra can be defined. However, to our knowledge so far no notion of domain or codomain has been investigated for fuzzy relations. These might, however, be useful, since fuzzy relations can, e.g., be used to model flow problems and many other things. We give a new axiomatisation of two variants of domain and codomain in the more general setting of idempotent left semirings that avoids complementation and hence is applicable to fuzzy relations. Some applications are sketched as well.

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Author:Jules Desharnais, Bernhard MöllerGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/58752
Parent Title (English):Lecture Notes in Computer Science
Publisher:Springer International
Place of publication:Cham
Year of first Publication:2014
Publishing Institution:Universität Augsburg
Release Date:2019/07/23
First Page:395
Last Page:411
Institutes:Fakultät für Angewandte Informatik
Fakultät für Angewandte Informatik / Institut für Informatik
Fakultät für Angewandte Informatik / Institut für Informatik / Professur für Programmiermethodik und Multimediale Informationssysteme
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Licence (German):Deutsches Urheberrecht