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Fuzzy graphs: Algebraic structure and syntactic recognition

Kalampakas, Antonios; Spartalis, Stefanos; Iliadis, Lazaros; Pimenidis, Elias

Authors

Antonios Kalampakas

Stefanos Spartalis

Lazaros Iliadis



Abstract

© Springer Science+Business Media Dordrecht 2013. Directed fuzzy hypergraphs are introduced as a generalization of both crisp directed hypergraphs and directed fuzzy graphs. It is proved that the set of all directed fuzzy hypergraphs can be structured into a magmoid with operations graph composition and disjoint union. In this framework a notion of syntactic recognition inside magmoids is defined. The corresponding class is proved to be closed under boolean operations and inverse mor-phisms of magmoids. Moreover, the language of all strongly connected fuzzy graphs and the language that consists of all fuzzy graphs that have at least one directed path from the begin node to the end node through edges with membership grade 1 are recognizable. Additionally, a useful characterization of recognizability through left derivatives is also achieved.

Journal Article Type Article
Publication Date Jan 1, 2014
Journal Artificial Intelligence Review
Print ISSN 0269-2821
Electronic ISSN 1573-7462
Publisher Springer (part of Springer Nature)
Peer Reviewed Peer Reviewed
Volume 42
Issue 3
Pages 479-490
APA6 Citation Kalampakas, A., Spartalis, S., Iliadis, L., & Pimenidis, E. (2014). Fuzzy graphs: Algebraic structure and syntactic recognition. Artificial Intelligence Review, 42(3), 479-490. https://doi.org/10.1007/s10462-013-9412-0
DOI https://doi.org/10.1007/s10462-013-9412-0
Keywords fuzzy graphs, hypergraphs, recognizability
Publisher URL http://dx.doi.org/10.1007/s10462-013-9412-0
Additional Information Additional Information : The final publication is available at Springer via http://dx.doi.org/10.1007/s10462-013-9412-0

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