On the use of the Choquet integral with fuzzy numbers in multiple criteria decision support

This paper presents a multiple criteria decision support approach in order to build a ranking and suggest a best choice on a set of alternatives. The partial evaluations of the alternatives on the points of view can be fuzzy numbers. The aggregation is performed through the use of a fuzzy extension of the Choquet integral. We detail how to assess the coefficients of the aggregation operator by using alternatives which are well-known to the decision maker, and which originate from his domain of expertise.

[1]  Mike Fitzpatrick.  Choice , 2004, The Lancet.

[2]  J. Barthélemy,et al.  Caractérisations axiomatiques de la distance de la différence symétrique entre des relations binaires , 1979 .

[3]  Jean-Luc Marichal,et al.  An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria , 2000, IEEE Trans. Fuzzy Syst..

[4]  Michel Grabisch,et al.  Fuzzy Measures and Integrals , 1995 .

[5]  G. Choquet.  Theory of capacities , 1954 .

[6]  P. Wakker.  Additive Representations of Preferences: A New Foundation of Decision Analysis , 1988 .

[7]  C. J. Hearne.  Non-conventional Preference Relations in Decision Making , 1989 .

[8]  Michel Grabisch,et al.  Application of the Choquet integral in multicriteria decision making , 2000 .

[9]  M. Kane.  Measurement theory. , 1980, NLN publications.

[10]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[11]  H. Carter.  Fuzzy Sets and Systems — Theory and Applications , 1982 .

[12]  Marc Roubens,et al.  Ranking and defuzzification methods based on area compensation , 1996, Fuzzy Sets Syst..

[13]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[14]  S. Orlovsky.  Decision-making with a fuzzy preference relation , 1978 .

[15]  V. Novák.  Fuzzy sets and their applications , 1989 .

[16]  Alain Chateauneuf,et al.  Some Characterizations of Lower Probabilities and Other Monotone Capacities through the use of Möbius Inversion , 1989, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[17]  Matthias Ehrgott,et al.  Multiple criteria decision analysis: state of the art surveys , 2005 .

[18]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

[19]  P. Vincke,et al.  Fuzzy Possibility Graphs and Their Application to Ranking Fuzzy Numbers , 1988 .

[20]  Michel Grabisch,et al.  K-order Additive Discrete Fuzzy Measures and Their Representation , 1997, Fuzzy Sets Syst..

[21]  Kwong-Sak Leung,et al.  Fuzzy numbers and fuzzification of the Choquet integral , 2005, Fuzzy Sets Syst..

[22]  Patrick Meyer,et al.  Sorting multi-attribute alternatives: The TOMASO method , 2005, Comput. Oper. Res..

[23]  Hung T. Nguyen,et al.  A note on the extension principle for fuzzy sets , 1978 .

[24]  Marc Roubens,et al.  Choice, Ranking and Sorting in Fuzzy Multiple Criteria Decision Aid , 2005 .

[25]  Jean-Luc Marichal,et al.  Aggregation of interacting criteria by means of the discrete Choquet integral , 2002 .

[26]  S. Orlovsky.  Decision-making with a fuzzy preference relation , 1978 .