No.
3
Project Title: An Algebraic Method to the Identification of Fuzzy Measures Based on Choquet Integrals
Adviser: Zhenyuan Wang
Description: This is concerning an inverse problem of the calculation of Choquet integrals, i.e., given the data of the integrand and the corresponding integration, how to determine the signed efficiency measure used in the Choquet integral. Reference [1] shows an iterative method to identify the fuzzy measure (monotone measures) from given data. However, that method cannot guarantee the convergence. A counterexample is needed to be cited. Moreover, an algebraic method can be developed for obtain the solution. Analyzing the complexity of the algorithm for the iterative method and making a comparison with the algebraic method are significant.
References:
[1] M. Grabisch, A new algorithm for identifying fuzzy measures and its application to pattern recognition, in Proc. FUZZ-IEEE/IFES, Yokohama, Japan, 1995, 145-150.
[2] Z. Wang, A new genetic algorithm for nonlinear multiregressions based on generalized Choquet integrals, Proc. FUZZ-IEEE2003, 819-821.
[3] Z. Wang and G. J. Klir, Fuzzy Measure
Theory, Plenum Press,
[4] W. L. Winston, Operations Research—Applications and Algorithms (Fourth edition), Duxbury Press, 2004.
Prerequisites: MATH 4300/8306, Math 4310/8316, MATH 8520/9110, programming language (i.e., C++).
Requirements: Constructing a mathematical model. Develop the relevant algorithm and programming it. Running the program(s) for testing data. Completing a research paper on this topic that may be submitted to some international conference or international journal.