Nonlinear Multiregressions Based on Choquet Integral for Data with both Numerical and Categorical Attributes.
Date of Award
Master of Arts (MA)
Dr. Zhengyuan Wang
Based on generalized Choquet integrals with respect to signed fuzzy measures, a model of nonlinear multiregression that can catch the interaction among predictive attributes toward the objective attribute can be established. In this model, some predictive attributes are numerical while the others are categorical. A numericalization technique is adopted to project each state of a categorical attribute that has more than two states to a multi-dimensional space optimally through a genetic algorithm, in which some regression coefficients are determined from data. To reduce the complexity of the genetic algorithm, the other regression coefficients such as the values of the signed fuzzy measure are determined by an algebraic method. In conclusion, this paper improves the previous relative work in several aspects: (1) Using a signed fuzzy measure to replace the generalized fuzzy measure such that the regression can more appropriately describe the relation among the objective attributes and the predictive attributes. (2) To reduce the complexity of the genetic algorithm that is used to search the optimal estimation of the regression coefficients, taking a part of the unknown regression coefficients, the values of the signed fuzzy measure, out from the chromosome involved in the genetic algorithm. (3) Optimally projecting the states of the categorical attribute(s) into a partial ordering space instead of a total ordering space as done in the previous work, to "numericalize" the categorical attribute(s) when there are more than two states for a predictive attribute.
Hui, Jin, "Nonlinear Multiregressions Based on Choquet Integral for Data with both Numerical and Categorical Attributes." (2005). Student Work. 3558.
A Thesis Presented to the Department of Mathematics and the Faculty of the Graduate College University of Nebraska In Partial Fulfillment of the Requirements for the Degree Master of Arts University of Nebraska at Omaha Copyright 2005 Jin Hui