Extended VIKOR method in comparison with outranking methods

The VIKOR method was developed to solve MCDM problems with conflicting and noncommensurable (different units) criteria, assuming that compromising is acceptable for conflict resolution, the decision maker wants a solution that is the closest to the ideal, and the alternatives are evaluated according to all established criteria. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria, and on proposing compromise solution (one or more). The VIKOR method is extended with a stability analysis determining the weight stability intervals and with trade-offs analysis. The extended VIKOR method is compared with three multicriteria decision making methods: TOPSIS, PROMETHEE, and ELECTRE. A numerical example illustrates an application of the VIKOR method, and the results by all four considered methods are compared.

[1]  Gwo-Hshiung Tzeng,et al.  Multiobjective Decision-Making Approach to Energy Supply Mix Decisions in Taiwan , 1994 .

[2]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .

[3]  R. S. Laundy,et al.  Multiple Criteria Optimisation: Theory, Computation and Application , 1989 .

[4]  椹木 義一,et al.  Theory of multiobjective optimization , 1985 .

[5]  H. Kunzi,et al.  Lectu re Notes in Economics and Mathematical Systems , 1975 .

[6]  W. R. Buckland,et al.  Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. , 1952 .

[7]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[8]  Ching-Lai Hwang,et al.  Fuzzy Multiple Attribute Decision Making - Methods and Applications , 1992, Lecture Notes in Economics and Mathematical Systems.

[9]  R. L. Keeney,et al.  Decisions with Multiple Objectives: Preferences and Value Trade-Offs , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[10]  Philippe Vincke,et al.  Multicriteria Decision-aid , 1993 .

[11]  Bertrand Mareschal,et al.  Prométhée: a new family of outranking methods in multicriteria analysis , 1984 .

[12]  Gwo-Hshiung Tzeng,et al.  Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS , 2004, Eur. J. Oper. Res..

[13]  Evangelos Triantaphyllou,et al.  Multi-criteria Decision Making Methods: A Comparative Study , 2000 .

[14]  E. Antonsson,et al.  USING INDIFFERENCE POINTS IN ENGINEERING DECISIONS , 2000 .

[15]  Douglas J. Morrice,et al.  A Multiple Attribute Utility Theory Approach to Ranking and Selection , 2001, Manag. Sci..

[16]  J. Marchal.  Cours d'economie politique , 1950 .

[17]  A. Pascu.  Operational research '81: J.P. Brans (Ed.) Proceedings of the Ninth IFORS International Conference on Operational Research, Hamburg, Germany, July 20–24, 1981, North-Holland, Amsterdam, 1981, xx + 984 pages, Dfl.250.000 , 1982 .

[18]  Lotfi A. Zadeh,et al.  Optimality and non-scalar-valued performance criteria , 1963 .

[19]  Bertrand Mareschal,et al.  Weight stability intervals in multicriteria decision aid , 1988 .

[20]  David L. Olson,et al.  Comparison of three multicriteria methods to predict known outcomes , 2001, Eur. J. Oper. Res..

[21]  F. B. Vernadat,et al.  Decisions with Multiple Objectives: Preferences and Value Tradeoffs , 1994 .

[22]  Gwo-Hshiung Tzeng,et al.  Multicriteria analysis of environmental quality in Taipei: public preferences and improvement strategies. , 2002, Journal of environmental management.

[23]  K. Yoon.  A Reconciliation Among Discrete Compromise Solutions , 1987 .

[24]  L. Duckstein,et al.  Multiobjective optimization in river basin development , 1980 .

[25]  M. Freimer,et al.  Some New Results on Compromise Solutions for Group Decision Problems , 1976 .

[26]  Marc Roubens,et al.  Multiple criteria decision making , 1994 .

[27]  Gwo-Hshiung Tzeng,et al.  Multicriteria Planning of Post‐Earthquake Sustainable Reconstruction , 2002 .

[28]  P. Yu.  A Class of Solutions for Group Decision Problems , 1973 .

[29]  Charles Gide,et al.  Cours d'économie politique , 1911 .

[30]  Jian-Bo Yang,et al.  Multiple Attribute Decision Making , 1998 .

[31]  S French,et al.  Multicriteria Methodology for Decision Aiding , 1996 .

[32]  B. Mareschal,et al.  Novel types of sensitivity analysis for additive MCDM methods , 1995 .