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

A Fuzzy Approach to Erroneous Inputs in Context-Free Language Recognition

Using fuzzy context-free grammars one can easily describe a finite number of ways to derive incorrect strings together with their degree of correctness. However, in general there is an infinite number of ways to perform a certain task wrongly. In this paper we introduce a generalization of fuzzy context-free grammars, the so-called fuzzy context-free $K$-grammars, to model the situation of making a finite choice out of an infinity of possible grammatical errors during each context-free derivation step. Under minor assumptions on the parameter $K$ this model happens to be a very general framework to describe correctly as well as erroneously derived sentences by a single generating mechanism. Our first result characterizes the generating capacity of these fuzzy context-free $K$-grammars. As consequences we obtain: (i) bounds on modeling grammatical errors within the framework of fuzzy context-free grammars, and (ii) the fact that the family of languages generated by fuzzy context-free $K$-grammars shares closure properties very similar to those of the family of ordinary context-free languages. The second part of the paper is devoted to a few algorithms to recognize fuzzy context-free languages: viz. a variant of a functional version of Cocke-Younger- Kasami's algorithm and some recursive descent algorithms. These algorithms turn out to be robust in some very elementary sense and they can easily be extended to corresponding parsing algorithms

Controlled Fuzzy Parallel Rewriting

We study a Lindenmayer-like parallel rewriting system to model the growth of filaments (arrays of cells) in which developmental errors may occur. In essence this model is the fuzzy analogue of the derivation-controlled iteration grammar. Under minor assumptions on the family of control languages and on the family of fuzzy languages in the underlying iteration grammar, we show (i) regular control does not provide additional generating power to the model, (ii) the number of fuzzy substitutions in the underlying iteration grammar can be reduced to two, and (iii) the resulting family of fuzzy languages possesses strong closure properties, viz. it is a full hyper-AFFL, i.e., a hyper-algebraically closed full Abstract Family of Fuzzy Languages

Algebraic Aspects of Families of Fuzzy Languages

We study operations on fuzzy languages such as union, concatenation, Kleene $\star$, intersection with regular fuzzy languages, and several kinds of (iterated) fuzzy substitution. Then we consider families of fuzzy languages, closed under a fixed collection of these operations, which results in the concept of full Abstract Family of Fuzzy Languages or full AFFL. This algebraic structure is the fuzzy counterpart of the notion of full Abstract Family of Languages that has been encountered frequently in investigating families of crisp (i.e., non-fuzzy) languages. Some simpler and more complicated algebraic structures (such as full substitution-closed AFFL, full super-AFFL, full hyper-AFFL) will be considered as well.\ud In the second part of the paper we focus our attention to full AFFL's closed under iterated parallel fuzzy substitution, where the iterating process is prescribed by given crisp control languages. Proceeding inductively over the family of these control languages, yields an infinite sequence of full AFFL-structures with increasingly stronger closure properties

Towards Robustness in Parsing - Fuzzifying Context-Free Language Recognition

We discuss the concept of robustness with respect to parsing a context-free language. Our approach is based on the notions of fuzzy language, (generalized) fuzzy context-free grammar and parser / recognizer for fuzzy languages. As concrete examples we consider a robust version of Cocke-Younger-Kasami's algorithm and a robust kind of recursive descent recognizer

Decision Making in the Medical Domain: Comparing the Effectiveness of GP-Generated Fuzzy Intelligent Structures

ABSTRACT: In this work, we examine the effectiveness of two intelligent models in medical domains. Namely, we apply grammar-guided genetic programming to produce fuzzy intelligent structures, such as fuzzy rule-based systems and fuzzy Petri nets, in medical data mining tasks. First, we use two context-free grammars to describe fuzzy rule-based systems and fuzzy Petri nets with genetic programming. Then, we apply cellular encoding in order to express the fuzzy Petri nets with arbitrary size and topology. The models are examined thoroughly in four real-world medical data sets. Results are presented in detail and the competitive advantages and drawbacks of the selected methodologies are discussed, in respect to the nature of each application domain. Conclusions are drawn on the effectiveness and efficiency of the presented approach

Dealing with natural language interfaces in a geolocation context

In the geolocation field where high-level programs and low-level devices coexist, it is often difficult to find a friendly user inter- face to configure all the parameters. The challenge addressed in this paper is to propose intuitive and simple, thus natural lan- guage interfaces to interact with low-level devices. Such inter- faces contain natural language processing and fuzzy represen- tations of words that facilitate the elicitation of business-level objectives in our context