Linguistic Approximation and Fuzzy Logic: Current Methods and a New Approach using Neural Networks

This thesis describes the problem of linguistic approximation in fuzzy logic and discusses the existing approaches with their strengths and weaknesses. After basic mathematical definitions (fuzzy sets and operations on them, different types of fuzzy sets, equality and similarity of fuzzy sets) are described, the thesis focuses on techniques for linguistic modelling by means of fuzzy set theory. The concept of a linguistic variable, which plays an important role in the context of linguistic modelling and linguistic approximation, is discussed. The problem of linguistic approximation is then defined and its applications are discussed. Great importance is attached on the evaluation of these approaches. Because none of the current methods is fully satisfactory, there is a demand for other approaches. The second part of the thesis is dedicated to a new approach to the problem of linguistic approximation proposed by the author using neural network technology. The motivation of this approach is based on the numerous weaknesses of the approaches to this problem. After a brief description of the neural network frameworks used in this thesis, the suggested procedure is described. Finally, the program designed within the scope of this thesis, which performs linguistic approximation by use of neural networks, will be presented and the results will be documented and evaluated.