Design of a qualitative classification model through fuzzy support vector machine with type-2 fuzzy expected regression classifier preset

Methods of qualitative analysis, such as qualitative classification, have gained importance as an essential complement of existing quantitative analysis in numerous fields. Only a few models have been developed to deal with qualitative inputs in the form of type-2 fuzzy(T2F) sets properly, given that traditional defuzzification method like the Karnik-Mendel algorithm performs dimensionality reduction at the cost of loss of information. To improve the situation, we define the expected value and variance of T2F set in this paper. By using a combination of them, we transfer the vertical three-dimensional uncertainty of T2F set to horizontal range uncertainty without much distortion of information. Additionally, current classification models are unsuitable to the partial classification problem if an output is not fully assigned to a single class. We build a comprehensive qualitative classification model based on fuzzy support vector machine (FSVM) combined with type-2 fuzzy expected regression (FER) to solve the partial classification problem as mentioned. This classifier (i.e. FER-FSVM) makes it possible to achieve the discrimination of output while characterizing membership for each class in terms of multidimensional qualitative inputs (attributes) in the form of T2F sets. FER-FSVM also can self-learn the data structure and shift between FER or FSVM for classification automatically, thus largely improving the efficiency of the classification process. The new model is almost 7 times more efficient than FSVM, as shown by our empirical experiments.