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MCDM - Basic Tools

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Part of the International Series in Operations Research & Management Science book series (ISOR, volume 85)

3. Concluding Remarks

That which of the characterizations presented in this chapter is used in an MCDM method depends on which of three possible ways to express preferences:
  • by selecting weights,

  • by selecting reference points,

  • by selecting constraints on outcome components,

is believed to suit theDMbest. EachMCDMmethod adopts an assumption with respect to this. In the next chapter we make use of the above distinction as a basis for a taxonomy of interactive MCDM methods.

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4. Annotated References

  1. Benayoun R., de Montgolfier J., Laritchev O., (1971), Linear programming with multiple objective functions: Step Method (STEM). Mathematical Programming, 1, 366–375.CrossRefGoogle Scholar
  2. Bowman V.J. Jr., (1976), On the relationship of the Tchebycheff norm and the efficient frontier of multiple-criteria objectives. In: Multiple Criteria Decision Making, (Thirez H., Zionts S., eds.), Lecture Notes in Economics and Mathematical Systems, 130, Springer Verlag, Berlin, 76–85.Google Scholar
  3. Choo E.U., Atkins D.R., (1983), Proper efficiency in nonconvex programming. Mathematics of Operations Research, 8, 467–470.MathSciNetCrossRefGoogle Scholar
  4. Geoffrion A.M., (1968), Proper efficiency and the theory of vector maximization. Journal of Mathematical Analysis and its Applications, 22, 618–630.zbMATHMathSciNetCrossRefGoogle Scholar
  5. Haimes Y.Y., Lasdon L.S., Wismer D.A., (1971), On bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Transactions on Systems, Man and Cybernetics, 1, 296–297.MathSciNetCrossRefGoogle Scholar
  6. Kaliszewski I., (1987), A modified weighted Tchebycheff metric for multiple objective programming. Computers and Operations Research, 14, 315–323.zbMATHMathSciNetCrossRefGoogle Scholar
  7. Kaliszewski I., (1994a), A theorem on nonconvex functions and its application to vector optimization. European Journal of Operations Research, 80, 439–449.CrossRefGoogle Scholar
  8. Kaliszewski I., (1994b), Quantitative Pareto Analysis by Cone Separation Technique. Kluwer Academic Publishers, Boston.Google Scholar
  9. Kaliszewski I., (2000), Using trade-off information in decision making algorithms. Computers & Operations Research, 27, 161–182.zbMATHMathSciNetCrossRefGoogle Scholar
  10. Steuer R.E. (1986), Multiple Criteria Optimization: Theory, Computation and Application. John Wiley & Sons, New York.Google Scholar
  11. Steuer R.E., Choo E.U., (1983), An interactive weighted Tchebycheff procedure for multiple objective programming. Mathematical Programming, 26, 326–344.MathSciNetGoogle Scholar
  12. Wierzbicki A.P., (1980), The use of reference objectives in multiobjective optimization. In: Multiple Criteria Decision Making; Theory and Applications, (Fandel G., Gal T., eds.), Lecture Notes in Economics and Mathematical Systems, 177, Springer Verlag, Berlin, 468–486.Google Scholar
  13. Wierzbicki A.P., (1986), On the completeness and constructiveness of parametric characterizations to vector optimization problems. OR Spectrum, 8, 73–87.zbMATHMathSciNetGoogle Scholar
  14. Wierzbicki A.P., (1990), Multiple criteria solutions in noncooperative game theory, Part III: Theoretical Foundations. Discussion Paper 288, Kyoto Institute of Economic Research, Kyoto University, Kyoto.Google Scholar

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© Springer Science+Business Media, Inc. 2006

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