Parameter estimation based on type-2 fuzzy clustering

In regression analysis, if the data can not satisfy all of the existing assumptions, it is requires to go beyond the classical analyzes in the parameter estimation process. In such cases, estimation methods based on fuzzy logic is preferred as alternative methods. One of the important steps in obtaining the solution based on the fuzzy logic in the problem of obtaining the model parameters is to determine the clusters bringing up the data set and to obtain the membership grades which will determine the contributions of the data in these clusters. In this study, parameter estimation based on type-2 fuzzy clustering is discussed. Firstly, type-1 fuzzy clustering problem was solved by the fuzzy c-means (FCM) method when the fuzzifier index m=2. Then the fuzzifier m index was defined as interval number in the form of m=[m_1 ,m_2] for obtain solutions based on type-2 fuzzy logic. The degrees of belonging to the sets of observations were determined by type-2 fuzzy clustering method. Degree of memberships obtained as a result of clustering based on type-1 and type-2 fuzzy logic are used as weight that determine the model contributions of observations and parameter estimation using these degree of membership is determined by the proposed algorithm. Finally, the estimation result of the type-1 and type-2 fuzzy clustering parameter were compared with the error criterion based on the difference between observed values and the predicted values. Keywords: Fuzzy Logic, Fuzzy C-Means (FCM) Algorithm, Type-2 Fuzzy Clustering, Parameter Estimation.