A Bibliography on Fuzzy Automata, Grammars and Lanuages

This bibliography contains references to papers on fuzzy formal languages, the generation of fuzzy languages by means of fuzzy grammars, the recognition of fuzzy languages by fuzzy automata and machines, as well as some applications of fuzzy set theory to syntactic pattern recognition, linguistics and natural language processing

Fuzzy graphs: Algebraic structure and syntactic recognition

© Springer Science+Business Media Dordrecht 2013. Directed fuzzy hypergraphs are introduced as a generalization of both crisp directed hypergraphs and directed fuzzy graphs. It is proved that the set of all directed fuzzy hypergraphs can be structured into a magmoid with operations graph composition and disjoint union. In this framework a notion of syntactic recognition inside magmoids is defined. The corresponding class is proved to be closed under boolean operations and inverse mor-phisms of magmoids. Moreover, the language of all strongly connected fuzzy graphs and the language that consists of all fuzzy graphs that have at least one directed path from the begin node to the end node through edges with membership grade 1 are recognizable. Additionally, a useful characterization of recognizability through left derivatives is also achieved

Image Understanding by Hierarchical Symbolic Representation and Inexact Matching of Attributed Graphs

We study the symbolic representation of imagery information by a powerful global representation scheme in the form of Attributed Relational Graph (ARG), and propose new techniques for the extraction of such representation from spatial-domain images, and for performing the task of image understanding through the analysis of the extracted ARG representation. To achieve practical image understanding tasks, the system needs to comprehend the imagery information in a global form. Therefore, we propose a multi-layer hierarchical scheme for the extraction of global symbolic representation from spatial-domain images. The proposed scheme produces a symbolic mapping of the input data in terms of an output alphabet, whose elements are defined over global subimages. The proposed scheme uses a combination of model-driven and data-driven concepts. The model- driven principle is represented by a graph transducer, which is used to specify the alphabet at each layer in the scheme. A symbolic mapping is driven by the input data to map the input local alphabet into the output global alphabet. Through the iterative application of the symbolic transformational mapping at different levels of hierarchy, the system extracts a global representation from the image in the form of attributed relational graphs. Further processing and interpretation of the imagery information can, then, be performed on their ARG representation. We also propose an efficient approach for calculating a distance measure and finding the best inexact matching configuration between attributed relational graphs. For two ARGs, we define sequences of weighted error-transformations which when performed on one ARG (or a subgraph of it), will produce the other ARG. A distance measure between two ARGs is defined as the weight of the sequence which possesses minimum total-weight. Moreover, this minimum-total weight sequence defines the best inexact matching configuration between the two ARGs. The global minimization over the possible sequences is performed by a dynamic programming technique, the approach shows good results for ARGs of practical sizes. The proposed system possesses the capability to inference the alphabets of the ARG representation which it uses. In the inference phase, the hierarchical scheme is usually driven by the input data only, which normally consist of images of model objects. It extracts the global alphabet of the ARG representation of the models. The extracted model representation is then used in the operation phase of the system to: perform the mapping in the multi-layer scheme. We present our experimental results for utilizing the proposed system for locating objects in complex scenes

Characterizations of recognizable picture series

AbstractThe theory of two-dimensional languages as a generalization of formal string languages was motivated by problems arising from image processing and pattern recognition, and also concerns models of parallel computing. Here we investigate power series on pictures. These are functions that map pictures to elements of a semiring and provide an extension of two-dimensional languages to a quantitative setting. We assign weights to different devices, ranging from picture automata to tiling systems. We will prove that, for commutative semirings, the behaviours of weighted picture automata are precisely alphabetic projections of series defined in terms of rational operations, and also coincide with the families of series characterized by weighted tiling or weighted domino systems