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Title: Review of fuzzy system models with an emphasis on fuzzy functions
Authors: Türkşen, İsmail Burhan
Keywords: fuzzy clustering
fuzzy functions
fuzzy system models
Type 1 and 2 fuzzy system models
Issue Date: 2009
Publisher: Sage Publications Ltd
Abstract: Fuzzy system modelling (FSM) is one of the most prominent tools that can be used to identify the behaviour of highly non-linear systems with uncertainty. In the past, FSM techniques utilized Type 1 fuzzy sets in order to capture the uncertainty in the system. However, since Type I fuzzy sets express the belongingness of a crisp value x' of an input variable x in a fuzzy set A by a crisp membership value mu(A)(x'), they cannot fully capture the uncertainties associated with higher-order imprecisions in identifying membership functions. In the future, we are likely to observe higher types of fuzzy sets, such as Type 2 fuzzy sets. The use of Type 2 fuzzy sets and linguistic logical connectives has drawn a considerable amount of attention in the realm of FSM in the last two decades. In this paper, we first review Type I fuzzy system models known as Zadeh, Takagi-Sugeno and Turksen models; then we review potentially future realizations of Type 2 fuzzy systems again under the headings of Zadeh, Takagi-Sugeno and Turksen fuzzy system models, in contrast to Type I fuzzy system models. Zadeh's and Takagi-Sugeno's models are essentially fuzzy rule base (FRB) models, whereas Turksen's models are essentially fuzzy function (FF) models. Type 2 fuzzy system models have a higher predictive power. One of the essential problems of Type 2 fuzzy system models is computational complexity. In data-driven FSM methods discussed here, a fuzzy C-means (FCM) clustering algorithm is used in order to identify the system structure, ie, either the number of fuzzy rules or alternately the number of FFs.
ISSN: 0142-3312
Appears in Collections:Endüstri Mühendisliği Bölümü / Department of Industrial Engineering
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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