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Generalization of domination structures and nondominated solutions in multicriteria decision making

  • K. Bergstresser
  • A. Charnes
  • P. L. Yu
Contributed Papers

Abstract

The concepts of domination structures and nondominated solutions are important in tackling multicriteria decision problems. We relax Yu's requirement that the domination structure at each point of the criteria space be a convex cone (Ref. 1) and give results concerning the set of nondominated solutions for the case where the domination structure at each point is a convex set. A practical necessity for such a generalization is discussed. We also present conditions under which a locally nondominated solution is also a globally nondominated solution.

Key Words

Domination structures nondominated solutions multicriteria decision making domination factors polyhedral domination sets 

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References

  1. 1.
    Yu, P. L.,Cone Convexity, Cone Extreme Points, and Nondominated Solutions in Decision Problems with Multiobjectives, Journal of Optimization Theory and Applications, Vol. 14, No. 3, 1974.Google Scholar
  2. 2.
    Charnes, A., andCooper, W. W.,Management Models and Industrial Applications of Linear Programming, Vol. 2, John Wiley and Sons, New York, New York, 1961.Google Scholar
  3. 3.
    Stoer, J., andWitzgall, C.,Convexity and Optimization in Finite Dimensions, I, Springer-Verlag, Berlin, Germany, 1970.Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • K. Bergstresser
    • 1
  • A. Charnes
    • 2
  • P. L. Yu
    • 3
  1. 1.Department of Pure and Applied MathematicsWashington State UniversityPullman
  2. 2.The University of Texas SystemAustin
  3. 3.Department of General BusinessUniversity of TexasAustin

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