Construction of aggregation operators for automated decision making via optimal interpolation and global optimization

Gleb Beliakov

doi:10.3934/jimo.2007.3.193

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2007, Volume 3, Issue 2: 193-208. Doi: 10.3934/jimo.2007.3.193

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Construction of aggregation operators for automated decision making via optimal interpolation and global optimization

Gleb Beliakov^1,

1.
School of Engineering and Information Technology, Deakin University, 221 Burwood Hwy, Burwood 3125

Received: August 2006

Revised: January 2007

Published: April 2007

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Abstract

This paper examines methods of pointwise construction of aggregation operators via optimal interpolation. It is shown that several types of application-specific requirements lead to interpolatory type constraints on the aggregation function. These constraints are translated into global optimization problems, which are the focus of this paper. We present several methods of reduction of the number of variables, and formulate suitable numerical algorithms based on Lipschitz optimization.

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Mathematics Subject Classification: Primary: 65K05, 41A29, 03E72, 65D05; Secondary: 41A63,90C26.

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