Cut sets as recognizable tree languages

  • Authors:

  • Björn Borchardt;Andreas Maletti;Branimir Šešelja;Andreja Tepavčević;Heiko Vogler

  • Affiliations:

  • Department of Computer Science, Dresden University of Technology, D-01062 Dresden, Germany;Department of Computer Science, Dresden University of Technology, D-01062 Dresden, Germany;Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia and Montenegro;Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia and Montenegro;Department of Computer Science, Dresden University of Technology, D-01062 Dresden, Germany

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2006

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Abstract

A tree series over a semiring with partially ordered carrier set can be considered as a fuzzy set. We investigate conditions under which it can also be understood as a fuzzified recognizable tree language. In this sense, sufficient conditions are presented which, when imposed, ensure that every cut set, i.e., the pre-image of a prime filter of the carrier set, is a recognizable tree language. Moreover, such conditions are also presented for cut sets of recognizable tree series.