Development of Fuzzy System Models

Öz

In this study, we first review the development of Fuzzy System Models in an historical perspective. “Fuzzy Rule Bases” proposed by Zadeh (1975), first were developed by Sugeno-Yasukawa (1993). Later Tagaki-Sugeno (1985) proposed models which has “Fuzzy Rulebases” on the left hand side and “Regression Equations” on the right hand side. Later on “Fuzzy Regression” models were proposed in place of “Fuzzy Rulebases”. First of these were proposed by Hathaway and Bezdek (1993) as "Fuzzy C-Regression Model". Secondly, Höppner and Klawonn (2003) proposed nonlinear versions of Hathaway and Bezdek (1993) model. Beyond these works, "Fuzzy Functions" were proposed by Türkşen (2008) in place of Hathaway and Bezdek (1993) and Höppner and Klawonn (2003) models. Further developments on “Fuzzy Functions” were proposed by Çelikyılmaz and Türkşen (2008-2009) in a variety of versions. An experimental assessment of all these models are also discussed in this study.

Anahtar Kelimeler

• Fuzzy rule bases
• Fuzzy functions
• Fuzzy regression
• Fuzzy clustering

Bulanık Sistem Modellerinin Gelişimi

Öz

Bu çalışmamızda, Bulanık Sistem Modelleri’nin tarihi gelişimi gözden geçirilecektir. Zadeh (1975) “Bulanık Kural Tabanları” teklif etmiş, ve bunları Sugeno-Yasukawa (1993) geliştirmiştir. Diğer bir yönden, Tagaki-Sugeno (1985) sağ tarafı “Kural Tabanı” sol tarafı “Regresyon Denklemi” olan modellerin gelişimi yönünde tekliflerde bulunmuşlardır. Daha sonraki yıllarda, “Kural Tabanları” yerine “Bulanık Regresyon” modelleri teklif edilmiştir. Bunların ilki Hathaway ve Bezdek, (1993) tarafından doğrusal “Bulanık C-Regresyon Modeli” [Fuzzy C-Regression Model, (FCRM)] olarak sunulmuştur ve Höppner ve Klawonn (2003), Hathaway ve Bezdek (1993) modelinin doğrusal olmayan (nonlinear) gelişimini teklif etmişlerdir. Bu çalışmalar ötesinde, Türkşen (2008) “Bulanık Fonksiyonlar” modelini Hathaway ve Bezdek (1993) ve Höppner ve Klawonn (2003) modelleri yerine yeni bir model yapısı olarak sunmuştur. Daha sonra Türkşen (2008)’in sunduğu “Bulanık Fonksiyonlar” çeşitli yönlerde Çelikyilmaz ve Türkşen (2008-2009) tarafından geliştirilmiştir.

Anahtar Kelimeler

• Bulanık kural tabanları
• Bulanık fonksiyonlar
• Bulanık regresyon
• Bulanık öbekleme

Kaynakça

1. Bezdek, J.C., 1981. Pattern Recognition with Fuzzy Objective Functions Algorithms. Kluwer Academic Publishers, Norwell, MA.
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4. Çelikyılmaz, A., Türkşen I.B., 2008. Uncertainty Modeling of Improved Fuzzy Functions With Evolutionary Systems. IEEE Trans. On Sys., Man & Cybern., 38(4): 1098-1110.
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9. Höppner, F., Klawonn, F., 2003. A Contribution to Convergence Theory of Fuzzy e-Means and Derivatives. IEEE Trans. on Fuzzy Systems, 11(5):682-694.
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