Fuzzy graphs: Algebraic structure and syntactic recognition

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

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
• Online Publication Date: Jul 11, 2013
• Publication Date: Oct 1, 2014
• Deposit Date: Nov 12, 2014
• Publicly Available Date: Nov 15, 2016
• 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
• DOI: https://doi.org/10.1007/s10462-013-9412-0
• Keywords: fuzzy graphs, hypergraphs, recognizability
• Public URL: https://uwe-repository.worktribe.com/output/810868
• 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
• Contract Date: Nov 15, 2016