General-Nondeterministic Fuzzy Pushdown Automata and Their Languages

Inspired by nondeterministic fuzzy finite automata theory proposed by Cao and Ezawa [1], we define general-nondeterministic fuzzy pushdown automata (GN-FPDAs). For a GN-FPDA, the fuzzy transition function in a state may have more than one transitions labeled by the same input symbol and stack symbol, which apparently reflects nondeterminism. Here, it is also shown that the set of fuzzy languages accepted by GN-FPDAs by final states is coincide with that accepted by GN-FPDAs by empty stack. Amazingly, with help of the Pumping lemma of fuzzy context-free languages, we elaborate that GN-FPDAs accept more kinds of languages than common fuzzy pushdown automata. Furthermore, we introduce general-nondeterministic fuzzy context-free grammars (GN-FCFGs) and investigate the relationship between GN-FPDAs and GN-FCFGs. In addition, taking advantage of GN-FCFGs, the closure properties of operations, such as union, intersection, concatenation and Kleene closure, on the set of fuzzy languages accepted by GN-FPDAs are discussed in detail.