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

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.
Citation: Gleb Beliakov. Construction of aggregation operators for automated decision making via optimal interpolation and global optimization. Journal of Industrial & Management Optimization, 2007, 3 (2) : 193-208. doi: 10.3934/jimo.2007.3.193
[1]

Muhammad Qiyas, Saleem Abdullah, Shahzaib Ashraf, Saifullah Khan, Aziz Khan. Triangular picture fuzzy linguistic induced ordered weighted aggregation operators and its application on decision making problems. Mathematical Foundations of Computing, 2019, 2 (3) : 183-201. doi: 10.3934/mfc.2019013

[2]

Harish Garg. Some robust improved geometric aggregation operators under interval-valued intuitionistic fuzzy environment for multi-criteria decision-making process. Journal of Industrial & Management Optimization, 2018, 14 (1) : 283-308. doi: 10.3934/jimo.2017047

[3]

Cheng-Kai Hu, Fung-Bao Liu, Cheng-Feng Hu. Efficiency measures in fuzzy data envelopment analysis with common weights. Journal of Industrial & Management Optimization, 2017, 13 (1) : 237-249. doi: 10.3934/jimo.2016014

[4]

Feyza Gürbüz, Panos M. Pardalos. A decision making process application for the slurry production in ceramics via fuzzy cluster and data mining. Journal of Industrial & Management Optimization, 2012, 8 (2) : 285-297. doi: 10.3934/jimo.2012.8.285

[5]

Kenji Nakanishi. Modified wave operators for the Hartree equation with data, image and convergence in the same space. Communications on Pure & Applied Analysis, 2002, 1 (2) : 237-252. doi: 10.3934/cpaa.2002.1.237

[6]

V. Pata, Sergey Zelik. A result on the existence of global attractors for semigroups of closed operators. Communications on Pure & Applied Analysis, 2007, 6 (2) : 481-486. doi: 10.3934/cpaa.2007.6.481

[7]

Jean Dolbeault, Maria J. Esteban, Michał Kowalczyk, Michael Loss. Improved interpolation inequalities on the sphere. Discrete & Continuous Dynamical Systems - S, 2014, 7 (4) : 695-724. doi: 10.3934/dcdss.2014.7.695

[8]

Charles Fefferman. Interpolation by linear programming I. Discrete & Continuous Dynamical Systems - A, 2011, 30 (2) : 477-492. doi: 10.3934/dcds.2011.30.477

[9]

Romina Gaburro, Clifford J Nolan. Enhanced imaging from multiply scattered waves. Inverse Problems & Imaging, 2008, 2 (2) : 225-250. doi: 10.3934/ipi.2008.2.225

[10]

Matthew S. Keegan, Berta Sandberg, Tony F. Chan. A multiphase logic framework for multichannel image segmentation. Inverse Problems & Imaging, 2012, 6 (1) : 95-110. doi: 10.3934/ipi.2012.6.95

[11]

T. L. Mason, C. Emelle, J. van Berkel, A. M. Bagirov, F. Kampas, J. D. Pintér. Integrated production system optimization using global optimization techniques. Journal of Industrial & Management Optimization, 2007, 3 (2) : 257-277. doi: 10.3934/jimo.2007.3.257

[12]

Dan Li, Li-Ping Pang, Fang-Fang Guo, Zun-Quan Xia. An alternating linearization method with inexact data for bilevel nonsmooth convex optimization. Journal of Industrial & Management Optimization, 2014, 10 (3) : 859-869. doi: 10.3934/jimo.2014.10.859

[13]

Rentsen Enkhbat, Evgeniya A. Finkelstein, Anton S. Anikin, Alexandr Yu. Gornov. Global optimization reduction of generalized Malfatti's problem. Numerical Algebra, Control & Optimization, 2017, 7 (2) : 211-221. doi: 10.3934/naco.2017015

[14]

Enkhbat Rentsen, J. Zhou, K. L. Teo. A global optimization approach to fractional optimal control. Journal of Industrial & Management Optimization, 2016, 12 (1) : 73-82. doi: 10.3934/jimo.2016.12.73

[15]

Giancarlo Bigi. Componentwise versus global approaches to nonsmooth multiobjective optimization. Journal of Industrial & Management Optimization, 2005, 1 (1) : 21-32. doi: 10.3934/jimo.2005.1.21

[16]

Chien-Wen Chao, Shu-Cherng Fang, Ching-Jong Liao. A tropical cyclone-based method for global optimization. Journal of Industrial & Management Optimization, 2012, 8 (1) : 103-115. doi: 10.3934/jimo.2012.8.103

[17]

Bun Theang Ong, Masao Fukushima. Global optimization via differential evolution with automatic termination. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 57-67. doi: 10.3934/naco.2012.2.57

[18]

Dmitri E. Kvasov, Yaroslav D. Sergeyev. Univariate geometric Lipschitz global optimization algorithms. Numerical Algebra, Control & Optimization, 2012, 2 (1) : 69-90. doi: 10.3934/naco.2012.2.69

[19]

Ahmet Sahiner, Nurullah Yilmaz, Gulden Kapusuz. A novel modeling and smoothing technique in global optimization. Journal of Industrial & Management Optimization, 2019, 15 (1) : 113-130. doi: 10.3934/jimo.2018035

[20]

Zhongliang Deng, Enwen Hu. Error minimization with global optimization for difference of convex functions. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1027-1033. doi: 10.3934/dcdss.2019070

2018 Impact Factor: 1.025

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (9)

Other articles
by authors

[Back to Top]