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

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

Received: 13 Jan 2011
Accepted: 23 Sep 2011
Published online: 29 Aug 2014 *

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