Fuzzy Tree Automata and Syntactic Pattern Recognition

An approach of representing patterns by trees and processing these trees by fuzzy tree automata is described. Fuzzy tree automata are defined and investigated. The results include that the class of fuzzy root-to-frontier recognizable Σ-trees is closed under intersection, union, and complementation. Thus, the class of fuzzy root-to-frontier recognizable Σ-trees forms a Boolean algebra. Fuzzy tree automata are applied to processing fuzzy tree representation of patterns based on syntactic pattern recognition. The grade of acceptance is defined and investigated. Quantitative measures of ``approximate isosceles triangle,'' ``approximate elongated isosceles triangle,'' ``approximate rectangle,'' and ``approximate cross'' are defined and used in the illustrative examples of this approach. By using these quantitative measures, a house, a house with high roof, and a church are also presented as illustrative examples. In addition, three fuzzy tree automata are constructed which have the capability of processing the fuzzy tree representations of ``fuzzy houses,'' ``houses with high roofs,'' and ``fuzzy churches,'' respectively. The results may have useful applications in pattern recognition, image processing, artificial intelligence, pattern database design and processing, image science, and pictorial information systems.