Volume 10, Number 18, December 2020

A Fuzzy BI-Objective Model for SVM with an Interactive Procedure to Identify the Best Compromise Solution

  Authors

Hager Ali Yahia¹, Mohammed Zakaria Moustafa¹, Mohammed Rizk Mohammed¹ and Hatem Awad Khater², ¹Alexandria University, Egypt, ²Horus University, Egypt

  Abstract

A support vector machine (SVM) learns the decision surface from two different classes of the input points. In many applications, there are misclassifications in some of the input points and each is not fully assigned to one of these two classes. In this paper a bi-objective quadratic programming model with fuzzy parameters is utilized and different feature quality measures are optimized simultaneously. An α-cut is defined to transform the fuzzy model to a family of classical bi-objective quadratic programming problems. The weighting method is used to optimize each of these problems. An important contribution will be added for the proposed fuzzy bi-objective quadratic programming model by getting different efficient support vectors due to changing the weighting values. The experimental results show the effectiveness of the α-cut with the weighting parameters on reducing the misclassification between two classes of the input points. An interactive procedure will be added to identify the best compromise solution from the generated efficient solutions.

  Keywords

Support vector machine (SVMs), Classification, Multi-objective problems, Weighting method, fuzzy mathematics, Quadratic programming, Interactive approach.