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Computing Min-Max Regret Solutions in Possibilistic Combinatorial Optimization Problems

  • Adam Kasperski
  • Paweł Zieliński
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 254)

Abstract

In this chapter we discuss a wide class of combinatorial optimization problems with a linear sum and a bottleneck cost function. We first investigate the case when the weights in the problem are modeled as closed intervals. We show how the notion of optimality can be extended by using a concept of a deviation interval. In order to choose a solution we adopt a robust approach. We seek a solution that minimizes the maximal regret, that is the maximal deviation from optimum over all weight realizations, called scenarios, which may occur. We then explore the case in which the weights are specified as fuzzy intervals. We show that under fuzzy weights the problem has an interpretation consistent with possibility theory. Namely, fuzzy weights induce a possibility distribution over the scenario set and the possibility and necessity measures can be used to extend the optimality evaluation and the min-max regret approach.

Keywords

Minimum Span Tree Combinatorial Optimization Problem Possibility Distribution Fuzzy Weight Fuzzy Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Adam Kasperski
    • 1
  • Paweł Zieliński
    • 2
  1. 1.Institute of Industrial Engineering and ManagementWrocław University of TechnologyWrocławPoland
  2. 2.Institute of Mathematics and Computer ScienceWrocław University of TechnologyWrocławPoland

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