Nondeterministic fuzzy automata

TL;DR

This paper introduces nondeterministic fuzzy automata, addressing the gap in representing nondeterminism within fuzzy automata, and proves their equivalence to deterministic fuzzy automata in language recognition.

Contribution

It defines nondeterministic fuzzy automata with and without epsilon-moves and establishes their equivalence to deterministic fuzzy automata in recognizing fuzzy languages.

Findings

Nondeterministic fuzzy automata are formally defined.

Equivalence between deterministic and nondeterministic fuzzy automata is proven.

All types recognize the same class of fuzzy languages.

Abstract

Fuzzy automata have long been accepted as a generalization of nondeterministic finite automata. A closer examination, however, shows that the fundamental property---nondeterminism---in nondeterministic finite automata has not been well embodied in the generalization. In this paper, we introduce nondeterministic fuzzy automata with or without $\el$-moves and fuzzy languages recognized by them. Furthermore, we prove that (deterministic) fuzzy automata, nondeterministic fuzzy automata, and nondeterministic fuzzy automata with $\el$-moves are all equivalent in the sense that they recognize the same class of fuzzy languages.