American Institute of Mathematical Sciences

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April  2007, 3(2): 193-208. doi: 10.3934/jimo.2007.3.193

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, Australia

Received  August 2006 Revised  January 2007 Published  April 2007

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.
Keywords: fuzzy logic, Aggregation operators, scattered data interpolation., global optimization.
Mathematics Subject Classification: Primary: 65K05, 41A29, 03E72, 65D05; Secondary: 41A63,90C2.
Citation: Gleb Beliakov. Construction of aggregation operators for automated decision making via optimal interpolation and global optimization. Journal of Industrial and Management Optimization, 2007, 3 (2) : 193-208. doi: 10.3934/jimo.2007.3.193
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