Fuzzy tree language recognizability

  • Authors:
  • Symeon Bozapalidis;Olympia Louscou Bozapalidoy

  • Affiliations:
  • Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece;Section of Mathematics and Informatics, Technical Institute of West Macedonia, Koila, Kozani, Greece

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2010

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Abstract

A fuzzy tree language with membership grades in an arbitrary set is syntactically recognizable (s-recognizable) if its syntactic algebra is finite. The equality problem for such languages is decidable and their syntactic algebra can be effectively constructed provided that they are s-recognizable. Linear (but non arbitrary) tree homomorphisms preserve s-recognizability. Tree automata whose transitions are weighted over the unit interval and whose behavior is computed with respect to a pair made of a t-norm distributive over a t-conorm have the syntactic recognition power and thus their equivalence problem is decidable. However, s-recognizability is more powerful when dealing with non-distributive pairs of such operations.