A Pumping Lemma for Fuzzy Tree Language with a Threshold

In this paper, at first, we recall some preliminaries related to tree automata. Then, we define fuzzy tree language with a threshold. Furthermore, a pumping lemma for fuzzy tree languages with a threshold is obtained. This lemma is extremely useful in proving that certain sets of ground trees are not recognizable. It is also useful for solving decision problems like emptiness and finiteness of are cognizable tree language. Our pumping lemma extends the pumping lemma obtained for fuzzy language and tree language. Also, we consider some decision problems such as emptiness problem and finiteness problem.