Nonlinear Integrals and Their Applications in Data Mining

非线性积分及其在数据挖掘中的应用：The theory of nonadditive set functions and relevant nonlinear integrals, as a new mathematics branch, has been developed for more than thirty years. Starting from the beginning of the nineties of the last century, several monographs were published. The first author of this monograph and Professor George J. Klir (The State University of New York at Binghamton) have published two books, Fuzzy Measure Theory (Plenum Press, New York, 1992) and Generalized Measure Theory (Springer-verlag, New York, 2008) on this top ic. These two books cover most of their theoretical research results with colleagues at the Chinese University of Hong Kong in the area of nonadditive set functions and relevant nonlinear integrals. Since the 1980s, nonadditive set functions and nonlinear integrals have been successfully applied in information fusion and data mining. However, only a few applications are involved in the above-mentioned books. As a supplement and indepth material, the current monograph, Nonlinear Integrals and Their Applications in Data Mining, concentrates on the applications in data analysis. Since the number of attributes in any database is always finite, we focus on our fundamentally theoretical discussion of nonadditive set function and nonlinear integrals, which are presented in the first several chapters, on the finite universal set, and abandon all convergence and limit theorems. ic. These two books cover most of their theoretical research results with colleagues at the Chinese University of Hong Kong in the area of nonadditive set functions and relevant nonlinear integrals. Since the 1980s, nonadditive set functions and nonlinear integrals have been successfully applied in information fusion and data mining. However, only a few applications are involved in the above-mentioned books. As a supplement and indepth material, the current monograph, Nonlinear Integrals and Their Applications in Data Mining, concentrates on the applications in data analysis. Since the number of attributes in any database is always finite, we focus on our fundamentally theoretical discussion of nonadditive set function and nonlinear integrals, which are presented in the first several chapters, on the finite universal set, and abandon all convergence and limit theorems.