In this chapter, we present a method for approximate evaluation of Zadeh's Z-numbers using category sets of probability distributions corresponding to similar certainty measures.

We present an iterative preprocessing approach for training a support vector machine for a large dataset, based on balancing the center of mass of input data within a variable margin about the hyperplane. At each iteration, the input data is projected on the hyperplane, and the imbalance of the center of mass for different classes within a variable margin is used to update the direction of the hyperplane within the feature space. The approach provides an estimate for the margin and the regularization constant. In the case of fuzzy membership of the data, the membership function of the input data is used to determine center of mass and to count data points which violate the margin. An extension of this approach to non-linear SVM is suggested based on dimension estimation of the feature space represented via a set of orthonormal feature vectors.