Abstract
Antimirov's partial derivatives are used in classical automata theory for the conversion of regular expressions to finite automata, tree regular expressions to tree automata, and ω-regular expressions to Buchi automata. In this paper, we describe a new variant of the Antimirov's partial derivatives for the conversion of fuzzy regular expressions to ε-free fuzzy non-deterministic finite automata. The membership values in fuzzy automata are assigned by using integral lattice-ordered monoids. The resulting automaton turns out to be an improvement over the existing approaches, because it is ε -free. Furthermore, herein it is formally proved that a non-deterministic fuzzy automaton M is obtained from a fuzzy regular expression r such that LR(M) LR(r).