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Generalization of domination structures and nondominated solutions in multicriteria decision making

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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.

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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.

  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.

  3. 3.

    Stoer, J., andWitzgall, C.,Convexity and Optimization in Finite Dimensions, I, Springer-Verlag, Berlin, Germany, 1970.

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Communicated by G. Leitmann

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Bergstresser, K., Charnes, A. & Yu, P.L. Generalization of domination structures and nondominated solutions in multicriteria decision making. J Optim Theory Appl 18, 3–13 (1976). https://doi.org/10.1007/BF00933790

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Key Words

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