Synthesizing fuzzy tree automata

Abstract

Fuzzy tree automata are mathematical devices for modeling and analyzing vaguely defined tree structures. The behavior of a fuzzy tree automaton generates a fuzzy tree language by mapping a set of regular trees on a ranked alphabet to fuzzy membership values. It calculates the membership grade of trees using a set of rules that process their structural characteristics. This paper deals with constructing fuzzy tree automata models that their behavior satisfies a set of given logical propositions (called properties) on the structure of trees. Our goal is uncertainty modeling by synthesizing fuzzy tree automata whose behavior is described by fuzzy linguistic variables. In this regard, we first provide several patterns and heuristic tricks and techniques for constructing fuzzy tree automata that satisfy simple properties. Then, we develop a method for modeling complex propositional formulas based on the conversion of a logical formula into a computation tree, as well as a step-by-step combination of models.