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Advances in cone-based preference modeling for decision making with multiple criteria

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Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Decision making with multiple criteria requires preferences elicited from the decision maker to determine a solution set. Models of preferences, that follow upon the concept of nondominated solutions introduced by Yu (1974), are presented and compared within a unified framework of cones. Polyhedral and nonpolyhedral, convex and nonconvex, translated, and variable cones are used to model different types of preferences. Common mathematical properties of the preferences are discussed. The impact of using these preferences in decision making is emphasized.
Rocznik
Strony
153--173
Opis fizyczny
Bibliogr. 52 poz., rys.
Twórcy
autor
  • Department of Mathematical Sciences, Clemson University, Clemson, SC USA
Bibliografia
  • 1. D. Baatar, M.M. Wiecek, Advancing equitability in multiobjective programming, Computers and Mathematics with Applications, 52 (2006) 1-2, 225–234.
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  • 4. V.Y. Blouin, B.J. Hunt, M.M. Wiecek, Relative importance of criteria in configuration design of vehicles, Department of Mathematical Sciences, Clemson University, Technical Report 2007.
  • 5. A. Cambini, D.T. Luc, L. Martein, Order-preserving transformations and applications, Journal of Optimization Theory and Applications, 118 (2003) 2, 275–293.
  • 6. G.Y. Chen, X. Huang, X. Yang, Vector Optimization. Set-valued and Variational Analysis. Springer, Berlin (2005).
  • 7. G.Y. Chen, X. Q. Yang, Characterization of variable domination structures via nonlinear scalarization, Journal of Optimization Theory and Applications, 112 (2002) 1, 97–110.
  • 8. K.L. Chew, Domination structures in abstract spaces, Southeast Asian Bulletin of Mathematics, Proceedings of the First Franco-Southeast Asian Mathematical Conference 2 (1979), 190–204.
  • 9. J. Dole&zcirc;al, Hierarchical solution concept for static and multistage decison problems with two objectives, Kybernetika 12 (1976) 5, 363–385.
  • 10. M. Ehrgott, M.M. Wiecek, Multiobjective Programming. In: Multiple Criteria Decision Analysis: State of the Art Surveys (eds. J. Figueira, S. Greco, and M. Ehrgott). Springer, New York, (2005), 667–722.
  • 11. A. Engau, Domination and Decomposition in Multiobjective Programming. PhD Thesis, Clemson University (2007).
  • 12. A. Engau, M.M. Wiecek, Cone characterizations of approximate solutions in real vector optimization, Journal of Optimization Theory and Applications 134 (2007) 3 (in press).
  • 13. A. Engau, M. M.Wiecek, Generating epsilon-efficient solutions in multiobjective programming, European Journal of Operational Research 177 (2007) 3, 1566–1579.
  • 14. A. Engau, M.M. Wiecek, Exact generation of epsilon-efficient solutions in multiple objective programming, OR Spectrum 29 (2007) 2, 335–350.
  • 15. A. Engau, M.M. Wiecek, 2D decision making for multi-criteria design optimization, Structural and Multidisciplinary Optimization 2007 (in press).
  • 16. J. Figueira, S. Greco, M. Ehrgott, Multiple Criteria Decision Analysis: State of the Art. Surveys, Springer, New York (2005).
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  • 18. B.J. Hunt, Multiobjective Programming with Convex Cones: Methodology and Applications. PhD Thesis, Clemson University (2004).
  • 19. B.J. Hunt, V.Y. Blouin, M.M. Wiecek, Modeling relative importance of design criteria with a modified Pareto preference, Journal of Mechanical Design, 2007 (in press).
  • 20. B.J. Hunt, M.M. Wiecek, Cones to aid decision making in multicriteria programming, In: Multiobjective Programming and Goal Programming (eds. T. Tanino, T. Tanaka, and M. Inuiguchi). Springer, Berlin, (2003), 153–158.
  • 21. B.J. Hunt, M.M. Wiecek, G. Fadel, Matrices as preference modeling tools in bi-criteria engineering design, 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, August-Sepetember AIAA (2004), 2004–4320.
  • 22. E.K. Karaskal,W.Michalowski, Incorporating wealth information into a multiple criteria decision making model, European Journal of Operational Research 150 (2003), 204–219.
  • 23. M.M. Kostreva, W. Ogryczak, Linear optimization with multiple equitable criteria, RAIRO Operations Research, 33 (1999) 3, 275–297.
  • 24. M.M. Kostreva, W. Ogryczak, A. Wierzbicki, Equitable aggregations in multiple criteria analysis, European Journal of Operational Research, 158 (2004) 2, 362–377.
  • 25. S.S. Kutateladze, Convex epsilon-programming, Soviet Mathematics. Doklady 20 (1979) 2, 391–393.
  • 26. S.A.Y. Lin, A comparison of Pareto optimality and domination structure, Metroeconimica, 28 (1976) 1-3, 62–74.
  • 27. P. Loridan, epsilon-Solutions in vector minimization problems, Journal of Optimization Theory and Applications, 43 (1984) 2, 265–276.
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  • 29. O.R. Men’shikova, V.V. Podinovskii, Constructing the preference relation and the core in multicriterion problems with inhomogenous criteria ordered by importance, U.S.S.R. Computational Matehmatics and Mathematical Physics 28 (1988) 3, 15–22.
  • 30. V.D. Noghin, Relative importance of criteria: A quantitative approach, Journal of Multi-criteria Decision Analysis, 6 (1997), 355–363.
  • 31. V.D. Noghin, I.V. Tolstykh, Using quantitative information on the relative importance of criteria for decision making, Computational Matehmatics and Mathematical Physics 40 (2000) 11, 1529–1536.
  • 32. W. Ogryczak, Multiple criteria linear programming model for portfolio selection, Annals of Operations Research, 97 (1997), 143–162.
  • 33. W. Ogryczak. Inequality measures and equitable approaches to location problems, European Journal of Operational Research, 122 (2000) 2, 374–391.
  • 34. W. Ogryczak, A. Wierzbicki, M. Milewski, A multi-criteria approach to fair and efficient bandwidth allocation, Omega 36 (2008) 3, 451–463.
  • 35. V.V. Podinovskii, Two-criterial problems with unequally rated criteria, Engineering Cybernetics 5 (1977), 44–59.
  • 36. V.V. Podinovskii, Importance coefficients of criteria in decision making problems: serial or ordinal importance coefficients, Automation and Remote Control 39 (1978) 10, 1514–1524.
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  • 38. V.V. Podinovskii, Quantitative importance of criteria, Automation and Remote Control 61 (2000) 5, 817–828.
  • 39. B. Roy, V. Mousseau, A theoretical framework for analyzing the notion of relative importance of criteria, Journal of Multi-criteria Decision Analysis, 5 (1996), 145–159.
  • 40. Y. Sawaragi, H. Nakayama, T. Tanino, Theory of Multiobjective Optimization. Academic Press, Orlando, 1985.
  • 41. V.K. Singh, Equitable Efficiency in Multiple Criteria Optimization. PhD Thesis, Clemson University 2007.
  • 42. E. Takeda, T. Nishida, Multiple criteria decision problems with fuzzy domination structures, Fuzzy Sets and Systems, 3 (1980) 123–136.
  • 43. Q. Wei, H. Yan, J. Ma, Z. Fan, A compromise weight for multicriteria group decision making with individual preference, Journal of Operational Research Society 51 (2000), 625–634.
  • 44. P. Weidner, Problems in scalarizing multicriteria approaches, In Multiple Criteria Decision Making in the New Millennium (eds. S. Zionts and and M. Koksalan). Springer, Berlin, (2001), 199-209.
  • 45. P. Weidner, Tradeoff directions and dominance sets, In: Multi–Objective Programming and Goal Programming (eds. T. Tanino, T. Tanaka, and M. Inuiguchi). Springer, Berlin, (2003), 275–280.
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  • 47. D.J. White, Epsilon efficiency, Journal of Optimization Theory and Applications 49 (1986) 2, 319–337.
  • 48. M.M. Wiecek, Multi-scenario multi-objective optimization for engineering design, In: Advances in Computational Optimization and its Applications (eds. K. Deb, P. Chakroborty, N.G.R. Iyengar, and S.K. Gupta). Universities Press, India, (2007), 170–174.
  • 49. H.C. Wu, A solution concept for fuzzy multiobjective programming problems based on convex cones, Journal of Optimization Theory and Applications 121 (2004) 2, 397–417.
  • 50. M.Q. Ying, The set of cone-extreme points and the grouping hierarchy problem, Journal of Systems Science and Mathematical Sciences 3 (1983) 2, 125–138.
  • 51. P.L. Yu, Cone convexity, cone extreme points and nondominated solutions in decision problems with multiobjectives. Journal of Optimization Theory and Applications, 14 (1974), 319–377.
  • 52. P.L. Yu, Multiple-Criteria Decision Making: Concepts, Techniques, and Extensions Plenum Press, New York 1985.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH8-0002-0033
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