Investigation of fuzzy functions approach and its possible applications in industrial engineering problems

Fuzzy set theory was introduced by Zadeh in 1965 as an extension to classical set theory. It has been a very important research subject for many researchers and has led to new developments for many fields since it enables to handle uncertainties successfully. One of these important developments is the fuzzy functions concept which was introduced by Professor I. Burhan Türkşen and combines fuzzy sets and fuzzy clustering concepts to provide an alternative solution approach to solve problems in diverse domains. The novelty of fuzzy functions is based on the fuzzy clustering concept and therefore based on fuzzy membership values. Fuzzy clustering is one of the corner stone of the fuzzy functions since finding the best partition constitutes the main problem in this approach. There are several fuzzy clustering algorithms in the literature which can be used in generating fuzzy functions. In this thesis Fuzzy c-Means (FCM) clustering algorithm is used in order to find out the membership values.One of the main motivations behind the development of the fuzzy functions approach was to overcome some of the drawbacks of the fuzzy rule bases which are one of the most frequently used fuzzy inference methods with many successful applications.As a contribution to the existing studies about fuzzy functions, first time in the present thesis we proposed to use genetic programming (GP) along with fuzzy clustering as a new approach in generating fuzzy functions. We used many data sets from the literature in order to present the application and the performance of our approach. We also performed comparisons with the existing fuzzy function generation methods like Least Square Estimation (LSE) in order to prove the validity of our approach. Based on the computational results we illustrated that fuzzy functions which are generated through genetic programming are very competitive and effective in many problem settings.Keywords: Fuzzy set theory, fuzzy rule bases (FRB), fuzzy clustering, fuzzy functions (FF), least square estimation (LSE), support vector machines (SVM), genetic programming (GP).