Simplifying the Minimax Disparity Model for Determining OWA Weights in Large-Scale Problems
In the context of multicriteria decision making, the ordered weighted averaging (OWA) functions play a crucial role in aggregating multiple criteria evaluations into an overall assessment supporting the decision makers’ choice. Determining OWA weights, therefore, is an essential part of this process. Available methods for determining OWA weights, however, often require heavy computational loads in real-life large-scale optimization problems. In this paper, we propose a new approach to simplify the well-known minimax disparity model for determining OWA weights. We use the binomial decomposition framework in which natural constraints can be imposed on the level of complexity of the weight distribution. The original problem of determining OWA weights is thereby transformed into a smaller scale optimization problem, formulated in terms of the coefficients in the binomial decomposition. Our preliminary results show that the minimax disparity model encoded with a small set of these coefficients can be solved in less computation time than the original model including the full-dimensional set of OWA weights.
KeywordsOrdered weighted averaging OWA weights determination Binomial decomposition framework k-additive level Large-scale optimization problems
The author would like to thank Ricardo Alberto Marques Pereira and Silvia Bortot for their helpful remarks on the manuscript. The author would like to thank to Andrea Mariello for his practical advice on the experiments. The author is grateful to the anonymous referees for their valuable suggestions.
- 3.Bortot, S., Fedrizzi, M., Marques Pereira, R.A., Nguyen, T.H.: The binomial decomposition of generalized Gini welfare functions, the S-Gini and Lorenzen cases. Inf. Sci. (to appear)Google Scholar
- 7.Carlsson, C., Fullér, R.: Maximal entropy and minimal variability OWA operator weights: a short survey of recent developments. In: Collan, M., Kacprzyk, J. (eds.) Soft Computing Applications for Group Decision-Making and Consensus Modeling, pp. 187–199. Springer, Heidelberg (2018)CrossRefGoogle Scholar
- 16.Mezei, J., Brunelli, M.: A closer look at the relation between orness and entropy of OWA function. In: Collan, M., Kacprzyk, J. (eds.) Soft Computing Applications for Group Decision-making and Consensus Modeling, Studies in Fuzziness and Soft Computing, pp. 201–211. Springer, Heidelberg (2018)Google Scholar
- 17.O’Hagan, M.: Aggregating template or rule antecedents in real-time expert systems with fuzzy set logic. In: Twenty-Second Asilomar Conference on Signals, Systems and Computers, vol. 2, pp. 681–689. IEEE (1988)Google Scholar