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Preliminaries

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

5. Concluding Remarks

With the material of this chapter we are well equipped to deal with issues of the next seven chapters. In fact, the notions defined up to now form a firm base for the subsequent presentations and developments and, except for some technical constructs, we shall not introduce any new concepts.

The notion of efficiency is quite intuitive. The notion of trade-off is less so (especially the notion of global trade-off) and the majority of works on MCDM exploit only the first notion without reference to the second. The rationale of using the notion of trade-off (point-to-point or global) in MCDM will be discussed in more detail in Chapter 4 and Chapter 6.

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6. Annotated References

  1. Chankong V., Haimes Y.Y., (1978), The interactive surrogate worth trade-off (ISWT) method for muliobjective decision-making. In: Multiple Criteria Problem Solving, (Zionts S., ed.), Lecture Notes in Economics and Mathematical Systems, 155, Springer-Verlag, Berlin, 42–67.Google Scholar
  2. Chankong V., Haimes Y.Y., (1983), Multiobjective Decision Making Theory and Methodology. Elsevier Science Publishing Co., New York.Google Scholar
  3. Cohon J.L., (1978), Multiobjective Programming and Planning. Academic Press, New York.Google Scholar
  4. Galas Z., Nykowski I., Żółkiewski Z., (1987), Multicriteria Programming (in Polish). Państwowe Wydawnictwo Ekonomiczne, Warszawa.Google Scholar
  5. Geoffrion A.M., (1968), Proper efficiency and the theory of vector maximization. Journal of Mathematical Analysis and its Applications, 22, 618–630.zbMATHMathSciNetCrossRefGoogle Scholar
  6. Guddat J., Guerra Vasquez F., Tammer K., Wendler K., (1985), Multiobjective and Stochastic Optimization Based on Parametric Optimization. Akademie-Verlag, Berlin.Google Scholar
  7. Haimes Y.Y., Hall W.A., Freedman H.T., (1975), Multiobjective Optimization in Water Resources Systems. Elsevier Scientific Publishing Company, Amsterdam.Google Scholar
  8. Haimes Y.Y., Tarvainen K., Shima T., Thadathil J., (1990), Hierarchical Multiobjective Analysis of Large-Scale Systems. Hemisphere Publishing Corporation, New York.Google Scholar
  9. Haimes Y.Y., Chankong V., (1979), Khun-Tucker multipliers as trade-offs in multiobjective decision-making analysis. Automatica, 15, 59–72.CrossRefGoogle Scholar
  10. Halme M., (1992), Local characterizations of efficient solutions in interactive multiple objective programming. Acta Academiae Oeconomicae Helsingiesis, Series A, 84.Google Scholar
  11. Henig M.I., Buchanan J., (1997), Tradeoff directions in multiobjective optimization problems. Mathematical Programming, 78, 357–374.MathSciNetCrossRefGoogle Scholar
  12. Hwang C.L., Masud A.S.M., Paidy S.R., Yoon K., (1979), Multiple Objective Decision Making — Methods and Applications. Lecture Notes in Economics and Mathematical Systems, 164, Springer Verlag, Berlin.Google Scholar
  13. Ignizio J.P., (1976), Goal Programming and Extensions. Lexington Books, D.C. Heath and Company.Google Scholar
  14. Ignizio J.P., (1985), Introduction to Linear Goal Programming. Sage Publications, Sage University Press, Beverly Hills.Google Scholar
  15. Jahn J., (1986), Mathematical Vector Optimization in Partially Ordered Linear Spaces, Peter Lang, Frankfurt am Main.Google Scholar
  16. Kaliszewski I., (1993), Calculating trade-offs by two-step parametric programming. Central European Journal of Operational Research and Economics, 2, 291–305.zbMATHGoogle Scholar
  17. Kaliszewski I., (1994b), Quantitative Pareto Analysis by Cone Separation Technique. Kluwer Academic Publishers, Boston.Google Scholar
  18. Kaliszewski I., Michalowski W., (1995), Generation of outcomes with selectively bounded tradeoffs. Foundations of Computing and Decision Sciences, 20, 113–122.MathSciNetGoogle Scholar
  19. Kaliszewski I., Michalowski W., (1997), Efficient solutions and bounds on tradeoffs. Journal of Optimization Theory and Applications, 94, 381–394.MathSciNetCrossRefGoogle Scholar
  20. Kaliszewski I., Michalowski W., (1999), Searching for psychologically stable solutions of multiple criteria decision problems. European Journal of Operational Research, 118, 549–562.CrossRefGoogle Scholar
  21. Keeney R.L., Raiffa H., (1976), Decisions with Multiple Objectives: Preferences and Value Tradeoffs. John Wiley & Sons, New York.Google Scholar
  22. Kuhn H.W., Tucker A., (1951), Nonlinear programming. Proceedings of the Second Berkeley Symposium on Mathematics, Statistics, and Probability, University of California Press, Berkeley.Google Scholar
  23. Lewandowski A., Wierzbicki A.P., (eds.), (1989), Aspiration Based Decision Support Systems, Theory, Software, Applications. Lecture Notes in Economics and Mathematical Systems, 331, Springer Verlag, Berlin.Google Scholar
  24. Luc D.T., (1989), Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems, 319, Springer Verlag, Berlin.Google Scholar
  25. Miettinen K.M., (1999), Nonlinear multiobjective optimization. Kluwer Academic Publishers, Dordrecht.Google Scholar
  26. Rietveld P., (1980), Objective Decision Methods and Regional Planning. North-Holland Publishing Company.Google Scholar
  27. Rniguest J.L., (1992), Multiobjective Optimization: Behavioral and Computational Considerations. Kluver Academic Publishers, Boston.Google Scholar
  28. Sakawa M., Yano H., (1990), Trade-off rates in the hyperplane method for multiple-objective optimization. European Journal of Operations Research, 44, 105–118.MathSciNetCrossRefGoogle Scholar
  29. Sawaragi Y., Nakayama H., Tanino T., (1985), Theory of Multiobjective Optimization. Academic Press, New York.Google Scholar
  30. Skulimowski A.M.J., (1996), Decision Support Systems Based on Reference Sets. AGH Publishers, Kraków.Google Scholar
  31. Stadler W., (1979), A survey of multicriteria optimization or the vector optimization problem, Part I (1776–1960). Journal of Optimization Theory and Applications, 29, 1–52.zbMATHMathSciNetCrossRefGoogle Scholar
  32. Steuer R.E. (1986), Multiple Criteria Optimization: Theory, Computation and Application. John Wiley & Sons, New York.Google Scholar
  33. Tabucanon M.T., (1988), Multiple Criteria Decision Making in Industry. Elsevier Science Publishers B.V., Amsterdam.Google Scholar
  34. Vincke P., (1992), Multicriteria Decision-Aid. JohnWiley & Sons, Inc., Chichester.Google Scholar
  35. 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
  36. Yoon K.P., Hwang C.-L., (1995), Multiple Attribute Decision Making: An Introduction. Sage Publications, Inc., Thousand Oaks.Google Scholar
  37. Yu P.L., (1985), Multiple Criteria Decision Making: Concepts, Techniques and Extensions. Plenum Press, New York.Google Scholar
  38. Zeleny M., (1982), Multiple Criteria Decision Making. McGraw-Hill, Inc.Google Scholar
  39. Zionts S., Wallenius J., (1976), An interactive programming method for solving the multiple criteria problem. Management Science, 22, 652–663.Google Scholar
  40. Zionts S., Walenius J., (1983), An interactive multiple objective linear programming method for a class of underlying nonlinear value functions. Management Science, 29, 519–529.MathSciNetCrossRefGoogle Scholar

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