Graph language recognizability is defined and investigated by virtue of the syntactic magmoid, analogously with the syntactic monoid of a word language. In this setup, the syntax complexity of a given recognizable graph language can be determined, giving rise to a syntactic classification inside the class of recognizable graph languages.
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… (More)
A new class of hypergroupoids, deriving from binary relations, is presented, via the introduced path hyperoperation. Its properties are investigated and its connections with Graph Theory are also delineated. Moreover, we present an application of this hyperoperation to assembly line designing and management.