Project 2

Project title: The Choquet integral with respect to fuzzy-valued set functions.

Adviser: Zhenyuan Wang

Description: The Choquet integral with respect to real-valued nonadditive set functions, such as signed efficiency measures, has been well developed and applied in information fusion and data mining successfully. However, in some real-world problems, the values of the involved set function may be not crisp but fuzzy. So, introducing the Choquet integral with respect to a fuzzy-valued set function, which is nonadditive usually, as an aggregation tool is useful in information fusion. It is also hopeful to be used in fuzzy information retrieval.

References:

[1] D. Denneberg, Non-Additive Measure and Integral, Kluwer, Boston, 1995

[2] G. J. Klir and B. Yuan, Fuzzy sets and Fuzzy Logic, Prentice-Hall, 1995.

[3] Z. Wang and G. J. Klir, Fuzzy Measure Theory, Plenum, New York, 1992.

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

Prerequisites: MATH 3230 or 4230, MATH 8370, MATH 8520.

Requirements: A theoretical analysis and calculation should be made. As a generalization the the Choquet integral with respect to real-valued set function, the new results should be concentrated in a research paper that can be submitted to some academic conference or journal.