Nonlinear nonnegative multiregressions based on Choquet integrals

Zhenyuan WANG; Kwong-Sak LEUNG; Man-Leung WONG; Jian FANG; Kebin XU

doi:10.1016/S0888-613X(00)00048-7

Nonlinear nonnegative multiregressions based on Choquet integrals

Zhenyuan WANG, Kwong-Sak LEUNG, Man-Leung WONG, Jian FANG, Kebin XU

Research output: Journal Publications › Journal Article (refereed) › peer-review

45 Citations (Scopus)

Abstract

Using a nonadditive set function to describe the interaction among attributes, a new nonlinear nonnegative multiregression is established based on Choquet integrals with respect to the set function. Regarding the values of the set function as unknown regression parameters, an evolutionary computation can be used to determine them when necessary data are available. Such a model is a generalization of the traditional linear multiregression. It provides an e€ective regression tool in some real problems where the linear multiregression model and the second-order multiregression model fail. This new method has a wide applicability in the areas of information fusion and data mining, as well as in the areas of decision making, image processing, pattern recognition, medical and industrial diagnoses, and expert systems.

Original language	English
Pages (from-to)	71-87
Number of pages	17
Journal	International Journal of Approximate Reasoning
Volume	25
Issue number	2
DOIs	https://doi.org/10.1016/S0888-613X(00)00048-7
Publication status	Published - Oct 2000
Externally published	Yes

Keywords

Nonlinear regressions
Information fusion
Data mining
Nonnegative monotone set functions
Choquet integrals
Optimization
Evolutionary algorithms

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10.1016/S0888-613X(00)00048-7

Cite this

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title = "Nonlinear nonnegative multiregressions based on Choquet integrals",

abstract = "Using a nonadditive set function to describe the interaction among attributes, a new nonlinear nonnegative multiregression is established based on Choquet integrals with respect to the set function. Regarding the values of the set function as unknown regression parameters, an evolutionary computation can be used to determine them when necessary data are available. Such a model is a generalization of the traditional linear multiregression. It provides an e€ective regression tool in some real problems where the linear multiregression model and the second-order multiregression model fail. This new method has a wide applicability in the areas of information fusion and data mining, as well as in the areas of decision making, image processing, pattern recognition, medical and industrial diagnoses, and expert systems.",

keywords = "Nonlinear regressions, Information fusion, Data mining, Nonnegative monotone set functions, Choquet integrals, Optimization, Evolutionary algorithms",

author = "Zhenyuan WANG and Kwong-Sak LEUNG and Man-Leung WONG and Jian FANG and Kebin XU",

year = "2000",

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T1 - Nonlinear nonnegative multiregressions based on Choquet integrals

AU - WANG, Zhenyuan

AU - LEUNG, Kwong-Sak

AU - WONG, Man-Leung

AU - FANG, Jian

AU - XU, Kebin

PY - 2000/10

Y1 - 2000/10

N2 - Using a nonadditive set function to describe the interaction among attributes, a new nonlinear nonnegative multiregression is established based on Choquet integrals with respect to the set function. Regarding the values of the set function as unknown regression parameters, an evolutionary computation can be used to determine them when necessary data are available. Such a model is a generalization of the traditional linear multiregression. It provides an e€ective regression tool in some real problems where the linear multiregression model and the second-order multiregression model fail. This new method has a wide applicability in the areas of information fusion and data mining, as well as in the areas of decision making, image processing, pattern recognition, medical and industrial diagnoses, and expert systems.

AB - Using a nonadditive set function to describe the interaction among attributes, a new nonlinear nonnegative multiregression is established based on Choquet integrals with respect to the set function. Regarding the values of the set function as unknown regression parameters, an evolutionary computation can be used to determine them when necessary data are available. Such a model is a generalization of the traditional linear multiregression. It provides an e€ective regression tool in some real problems where the linear multiregression model and the second-order multiregression model fail. This new method has a wide applicability in the areas of information fusion and data mining, as well as in the areas of decision making, image processing, pattern recognition, medical and industrial diagnoses, and expert systems.

KW - Nonlinear regressions

KW - Information fusion

KW - Data mining

KW - Nonnegative monotone set functions

KW - Choquet integrals

KW - Optimization

KW - Evolutionary algorithms

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DO - 10.1016/S0888-613X(00)00048-7

M3 - Journal Article (refereed)

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SP - 71

EP - 87

JO - International Journal of Approximate Reasoning

JF - International Journal of Approximate Reasoning

SN - 0888-613X

IS - 2

ER -

Nonlinear nonnegative multiregressions based on Choquet integrals

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Keywords

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