Project 3

Project title: Identification of monotone measures

Adviser: Zhenyuan Wang

Description: Based on an existing data set, to optimally determine a monotone measure defined on the power set of a given finite universal set, an algorithm with soft computing technique can be developed. In the algorithm, the crux is how to guarantee the monotonicity of the obtained set function. In this connection, a sub-algorithm called reordering algorithm should be embedded. According to the lattice structure of the power set of the given universal set, a max-min strategy is adopted in the embedded algorithm to reduce the computation complexity.

References:

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

[2] 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.

[3] 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, computational programming.

Requirements: A theoretical analysis and discussion should be made. A genetic algorithm with a reordering algorithm should be developed. By using a testing example, the established mathematical model and the algorithm should be justified. All results obtained in this project should be presented in a research paper that can be submitted to some academic conference or journal.