Abstract
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 morphisms 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.
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Arnold A, Dauchet M (1978) Théorie des magmoides. I. RAIRO Inform Théor 12:235–257
Arnold A, Dauchet M (1979) Théorie des magmoides. II. RAIRO Inform Théor 13:135–154
Blume C (2010) Recognizable graph languages for the verification of dynamic systems. In: LNCS 6372, pp 384–387
Blume C, Bruggink HJS, Friedrich M, König B (2012) Treewidth, pathwidth and cospan decompositions with applications to graph-accepting tree automata. J Vis Lang Comput. doi:10.1016/j.jvlc.2012.10.002
Bozapalidis S, Kalampakas A (2003) A finite complete set of equations generating graphs. Discret Math Theor Comput Sci LNCS 2731:118–128
Bozapalidis S, Kalampakas A (2004) An axiomatization of graphs. Acta Inform 41:19–61
Bozapalidis S, Kalampakas A (2005) Automata on patterns and graphs. In: Proceedings of the 1st international conference on algebraic informatics, pp 31–52. Aristotle University of Thessaloniki
Bozapalidis S, Bozapalidou OL (2006) On the recognizability of fuzzy languages. I. Fuzzy Sets Syst 157:2394–2402
Bozapalidis S, Kalampakas A (2006) Recognizability of graph and pattern languages. Acta Inform 42:553–581
Bozapalidis S, Bozapalidou OL (2008) On the recognizability of fuzzy languages. II. Fuzzy Sets Syst 159:107–113
Bozapalidis S, Kalampakas A (2008) Graph automata. Theor Comput Sci 393:147–165
Bozapalidis S, Bozapalidou OL (2010) Fuzzy tree language recognizability. Fuzzy Sets Syst 161:716–734
Bruggink HJS, König B (2010) A logic on subobjects and recognizability. IFIP-AICT 323:197–212
Brzozowski J, Ye Y (2011) Syntactic complexity of ideal and closed languages. In: LNCS 6795, pp 117–128
Brzozowski J, Li B, Ye Y (2012) Syntactic complexity of prefix-, suffix-, bifix-, and factor-free regular languages. Theor Comput Sci 449:37–53
Courcelle B (1990) The monadic second-order logic of graphs. I. Recognizable sets of finite graphs. Inform Comput 85:12–75
Courcelle B, Weil P (2005) The recognizability of sets of graphs is a robust property. Theor Comput Sci 342:173–228
Eilenberg S (1974) Automata, languages and machines, vol A. Academic Press, London
Engelfriet J, Vereijken JJ (1997) Context-free graph grammars and concatenation of graphs. Acta Inform 34:773–803
Ésik Z, Liu G (2007) Fuzzy tree automata. Fuzzy Sets Syst 158:1450–1460
Glykas M (ed) (2010) Fuzzy cognitive maps, advances in theory, methodologies, tools and applications. Springer, Berlin, Heidelberg
Gécseg F, Steinby M (1984) Tree automata. Akademiai Kiado, Budapest
Kalampakas A (2007) The syntactic complexity of Eulerian graphs. In: Proceedings of the 2nd international conference on algebraic informatics. LNCS 4728, pp 208–217
Kalampakas A (2011) Graph automata: the algebraic properties of abelian relational graphoids. In: LNCS 7020, pp 168–182
Kuich W, Rahonis G (2006) Fuzzy regular languages over finite and infinite words. Fuzzy Sets Syst 157:1532–1549
Konstandinidis S, Sântean N, Yu S (2007) Fuzzification of rational and recognizable sets. Fundam Inform 76:413–447
Louskou-Bozapalidou O (2007) Non-deterministic recognizability of fuzzy languages. Appl Math Sci 1:821–826
Mordeson JN, Nair PS (2000) Fuzzy graphs and fuzzy hypergraphs. Physica-Verlag, Heidelberg
Mordeson JN, Malik D (2002) Fuzzy automata and languages: theory and applications. Chapman & Hall/CRC, London
Malik DS, Mordeson JN, Sen MK (1999) Minimization of fuzzy finite automata. Inf Sci 113:323–330
Petković T (2005) Varietes of fuzzy languages. In: Proceedings of the 1st international conference on algebraic informatics, pp 197–205. Aristotle University of Thessaloniki
Quernheim D, Knight K (2012) Towards probabilistic acceptors and transducers for feature structures. In: Proceedings of the 6th workshop syntax, semantics and structure in statistical translation, pp 76–85. Association for, computational linguistics, 2012
Rosenfeld A (1975) Fuzzy graphs. In: Zadeh LA, Fu KS, Tanaka K, Shimura M (eds) Fuzzy sets and their applications to cognitive and decision processes. Academic Press, New York, pp 77–95
Rahonis G (2005) Infinite fuzzy computations. Fuzzy Sets Syst 153:275–288
Rahonis G (2009) Fuzzy Languages. In: Handbook of weighted automata, monographs in theoretical computer science, pp 481–517
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
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Kalampakas, A., Spartalis, S., Iliadis, L. et al. Fuzzy graphs: algebraic structure and syntactic recognition. Artif Intell Rev 42, 479–490 (2014). https://doi.org/10.1007/s10462-013-9412-0
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DOI: https://doi.org/10.1007/s10462-013-9412-0