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On Solving Optimization Problems with Ordered Average Criteria and Constraints

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Fuzzy Optimization

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 254))

Abstract

The problem of aggregating multiple numerical attributes to form overall measure is of considerable importance in many disciplines. The ordered weighted averaging (OWA) aggregation, introduced by Yager, uses the weights assigned to the ordered values rather than to the specific attributes. This allows one to model various aggregation preferences, preserving simultaneously the impartiality (neutrality) with respect to the individual attributes. However, importance weighted averaging is a central task in multiattribute decision problems of many kinds. It can be achieved with theWeighted OWA (WOWA) aggregation though the importanceweightsmake the WOWA concept much more complicated than the original OWA. In this paper we analyze solution procedures for optimization problems with the ordered average objective functions or constraints. We show that the WOWA aggregation with monotonic preferential weights can be reformulated in a way allowing to introduce linear programming optimization models, similar to the optimization models we developed earlier for the OWA aggregation. Computational efficiency of the proposed models is demonstrated.

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Authors and Affiliations

  1. Institute of Control & Computation Engineering, Warsaw University of Technology, 00-665, Warsaw, Poland

    Włodzimierz Ogryczak & Tomasz Śliwiński

Authors
  1. Włodzimierz Ogryczak
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  2. Tomasz Śliwiński
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Editor information

Editors and Affiliations

  1. Department of Mathemaitical and Statistical Sciences, University of Colorado Denver, PO Box 173364, 80217-3364, Colorado, Denver, USA

    Weldon A. Lodwick

  2. Systems Research Institute Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

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Ogryczak, W., Śliwiński, T. (2010). On Solving Optimization Problems with Ordered Average Criteria and Constraints. In: Lodwick, W.A., Kacprzyk, J. (eds) Fuzzy Optimization. Studies in Fuzziness and Soft Computing, vol 254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13935-2_10

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  • DOI: https://doi.org/10.1007/978-3-642-13935-2_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13934-5

  • Online ISBN: 978-3-642-13935-2

  • eBook Packages: EngineeringEngineering (R0)

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