Project 1

Project title: A nonlinear multiregression model based on the Choquet integral with a quadratic core

Adviser: Zhenyuan Wang

Description: The signed efficiency measures have been successfully used to describe the interaction among the contributions from predictive attributes towards the objective attribute. Hence, the nonlinear multiregression based on the Choquet integral with respect to a signed efficiency measure can capture such kind of interaction. When the core of the Choquet integral is linear, the captured interaction is only its linear part. So, if a quadratic core is adopted in the Choquet integral, the relevant regression model will be more powerful. It is a generalization of the existing nonlinear multiregression based on the Choquet integral as well as the traditional linear multiregression model. A soft computing technique, such as the genetic algorithm, is expected to be used for solving this new regression problem.

References:

[1] Z. Wang and H. Guo, A new genetic algorithm for nonlinear multiregressions based on generalized Choquet integrals, Proc. FUZZ-IEEE2003, 819-821.

[2] Z. Wang and G. J. Klir, Generalized Measure Theory, Springer, New York, 2008.

[3] Z. Wang, K. S. Leung, and G. J. Klir, Applying fuzzy measures and nonlinear integrals in data mining, (invited paper for 40 Anuv.). Fuzzy Sets and Systems 156 (2005), 371-380.

[4] Z. Wang, K. S. Leung, M. L. Wong, J. Fang, and K. Xu, Nonlinear nonnegative multi-regressions based on Choquet integrals, International Journal of Approximate Reasoning 25 (2000), 71-87.

Prerequisites: MATH 3230 or 4230, MATH 8520, programming language, computer graphic.

Requirements: A new nonlinear multiregression model based on the Choquet integral with a quadratic core should be established. The relevant algorithm should be developed. A research paper that can be submitted to some academic conference or journal is required. Some examples with graphics should be presented in the paper to show the effectiveness of the algorithm.