Int. J. of Granular Computing, Rough Sets and Intelligent Systems   »   2012 Vol.2, No.3

 

 

Title: A non-linear multi-regression model based on the Choquet integral with a quadratic core

 

Authors: Nian Yan; Zhengxin Chen; Yong Shi; Zhenyuan Wang

 

Addresses:
College of Information Science and Technology, University of Nebraska, Omaha, NE, 68182, USA.
College of Information Science and Technology, University of Nebraska, Omaha, NE, 68182, USA.
College of Information Science and Technology, University of Nebraska, Omaha, NE, 68182, USA; Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, 100080, Beijing, China.
Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, 100080, Beijing, China; Department of Mathematics, University of Nebraska, Omaha, NE, 68182, USA

 

Abstract: Signed efficiency measures with relevant non-linear integrals can be used to treat data that have strong interaction among contributions from various attributes towards a certain objective attribute. The Choquet integral is the most common non-linear integral. The non-linear multi-regression based on the Choquet integral can well describe the non-linear relation how the objective attribute depends on the predictive attributes. This research is to extend the non-linear multi-regression model from using a linear core to adopting a quadratic core in the Choquet integral. It can describe some more complex interaction among attributes and, therefore, can significantly improve the accuracy of non-linear multi-regression. The unknown parameters of the model involve the coefficients in the quadratic core and the values of the signed efficiency measure. They should be optimally determined via a genetic algorithm based on the given data. The results of the new model are compared with that of the linear core as well as the classic linear multi-regression that can be solved by an algebraic method.

 

Keywords: nonlinear models; multi-regression models; efficiency measure; Choquet integral; modelling; signed efficiency measure; genetic algorithms.

 

DOI: 10.1504/IJGCRSIS.2012.047018

 

Int. J. of Granular Computing, Rough Sets and Intelligent Systems, 2012 Vol.2, No.3, pp.244 - 256

 

Date of acceptance: 23 Sep 2011
Available online: 24 May 2012

 

 

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