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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Metadaten
Author:Jules Desharnais, Bernhard MöllerGND
URN:urn:nbn:de:bvb:384-opus4-587522
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/58752
ISBN:9783319062501OPAC
ISBN:9783319062518OPAC
ISSN:0302-9743OPAC
ISSN:1611-3349OPAC
Parent Title (English):Lecture Notes in Computer Science
Publisher:Springer International
Place of publication:Cham
Type:Article
Language:English
Year of first Publication:2014
Publishing Institution:Universität Augsburg
Release Date:2019/07/23
Volume:8428
First Page:395
Last Page:411
DOI:https://doi.org/10.1007/978-3-319-06251-8_24
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