Weighted grammars and Kleene's theorem
Information Processing Letters
On a generalization of fuzzy algebras and congruences
Fuzzy Sets and Systems
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Partially ordered and relational valued fuzzy relations I
Fuzzy Sets and Systems - Special issue on fuzzy relations, part 1
Handbook of formal languages, vol. 3
Completion of ordered structures by cuts of fuzzy sets: an overview
Fuzzy Sets and Systems - Logic and algebra
Representing ordered structures by fuzzy sets: an overview
Fuzzy Sets and Systems - Logic and algebra
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the workshop weighted automata: Theory and applications (Dresden University of Technology (Germany), March 4-8, 2002)
A Kleene Theorem for Weighted Tree Automata
Theory of Computing Systems
Weighted tree automata and weighted logics
Theoretical Computer Science
Cut sets as recognizable tree languages
Fuzzy Sets and Systems
Weighted finite automata over strong bimonoids
Information Sciences: an International Journal
Myhill--Nerode type theory for fuzzy languages and automata
Fuzzy Sets and Systems
On lattice valued up-sets and down-sets
Fuzzy Sets and Systems
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The topic of this short note is tree series over semirings with partially ordered carrier set. Thus, tree series become poset-valued fuzzy sets. Starting with a collection of recognizable tree languages we construct a tree series recognizable over any semiring, such that the carrier set is a poset generated by the collection. In the framework of fuzzy structures, the starting collection becomes a subset of the collection of the corresponding cut sets. Under some stricter conditions, it is even equal to this collection. We also partially solve an open problem which was posed in Borchardt et al. [Cut sets as recognizable tree languages, Fuzzy Sets and Systems 157 (2006) 1560-1571]. Namely, we show that if @f is a given tree series over a partially ordered, locally finite semiring A, then @f is recognizable if and only if there are finitely many cut sets of @f and every cut set is a recognizable tree language.