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A New Optimization Approach to Clustering Fuzzy Data for Type-2 Fuzzy System Modeling
Abstract
This chapter presents a new optimization method for clustering fuzzy data to generate Type-2 fuzzy system models. For this purpose, first, a new distance measure for calculating the (dis)similarity between fuzzy data is proposed. Then, based on the proposed distance measure, Fuzzy c-Mean (FCM) clustering algorithm is modified. Next, Xie-Beni cluster validity index is modified to be able to valuate Type-2 fuzzy clustering approach. In this index, all operations are fuzzy and the minimization method is fuzzy ranking with Hamming distance. The proposed Type-2 fuzzy clustering method is used for development of indirect approach to Type-2 fuzzy modeling, where the rules are extracted from clustering fuzzy numbers (Zadeh, 1965). Then, the Type-2 fuzzy system is tuned by an inference algorithm for optimization of the main parameters of Type-2 parametric system. In this case, the parameters are: Schweizer and Sklar t-Norm and s-Norm, a-cut of rule-bases, combination of FATI and FITA inference approaches, and Yager parametric defuzzification. Finally, the proposed Type-2 fuzzy system model is applied in prediction of the steel additives in steelmaking process. It is shown that, the proposed Type-2 fuzzy system model is superior in comparison with multiple regressions and Type-1 fuzzy system model, in terms of the minimization the effect of uncertainty in the rule-base fuzzy system models an error reduction.
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