Parameter Estimation By Type-2 Fuzzy Logic In Case That Data Set Has Outlier

Abstract

One of the problems encountered in estimating the unknown parameters of the regression models is the presence of outliers in the data set. This situation may cause problems in providing some assumptions such as the normal distribution for the parameter estimation process and the homogeneity of the variances. The case of the presence of outlier observations in the data set, estimation methods based on fuzzy logic that can be minimized the level of impact of this data are emerged as available methods. If fuzzy logic is used in regression analysis, there are two main steps for parameter estimation. The first of these is to define the clusters that compose the data set, and the other is calculate the degree of membership to determining the contributions of the data to each model for the clusters. In this study, type-2 fuzzy clustering algorithm defined as an expansion of fuzzy c-means algorithm in the determination of membership degrees of data sets was benefited. The presence of outliers in the data set is addressed. An algorithm has been proposed to estimate the unknown belonging to parameters of the regression model using the membership degrees obtained relating to the cluster elements. The parameters were estimated using regression methods to examine the effectiveness of the algorithm that called robust methods, and the results obtained were compared.