On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application

Abstract We consider the use of the Choquet integral for evaluating projects or actions in a real-world application starting from the case of the re-qualification of an abandoned quarry. Despite the Choquet integral being a very well-known preference model for which there is a rich and well developed theory, its application in a multiple criteria decision aiding perspective requires some specific methodological developments. This led us to work out and implement in practice two new procedures: a first procedure to build interval scales with the objective of assigning utility values on a common scale to the criteria performances, and a second one to construct a ratio scale for assigning numerical values to the capacities of the Choquet integral. This article discusses the strengths and weaknesses of the Choquet integral as appearing in the case study, proposing as well insights related to the interaction of the experts within a focus group.

[1]  José Rui Figueira,et al.  Dealing with a multiple criteria environmental problem with interaction effects between criteria through an extension of the Electre III method , 2015, Eur. J. Oper. Res..

[2]  Jean-Luc Marichal,et al.  Determination of weights of interacting criteria from a reference set , 2000, Eur. J. Oper. Res..

[3]  Michel Grabisch,et al.  A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid , 2010, Ann. Oper. Res..

[4]  M. Budden.  Focus groups: Theory and practice , 1999 .

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

[6]  Michel Grabisch,et al.  Equivalent Representations of Set Functions , 2000, Math. Oper. Res..

[7]  P. Vincke,et al.  Relational Systems of Preference with One or More Pseudo-Criteria: Some New Concepts and Results , 1984 .

[8]  Bernard Roy,et al.  Determining the weights of criteria in the ELECTRE type methods with a revised Simos' procedure , 2002, Eur. J. Oper. Res..

[9]  José Rui Figueira,et al.  ELECTRE methods with interaction between criteria: An extension of the concordance index , 2009, Eur. J. Oper. Res..

[10]  Katsushige Fujimoto,et al.  Representations of Importance and Interaction of Fuzzy Measures, Capacities, Games and Its Extensions: A Survey , 2010, IUM.

[11]  Jacques Pictet,et al.  Extended use of the cards procedure as a simple elicitation technique for MAVT. Application to public procurement in Switzerland , 2008, Eur. J. Oper. Res..

[12]  Salvatore Greco,et al.  Stochastic multiobjective acceptability analysis for the Choquet integral preference model and the scale construction problem , 2013, Eur. J. Oper. Res..

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

[14]  M. Grabisch.  The application of fuzzy integrals in multicriteria decision making , 1996 .

[15]  Ivan Kojadinovic,et al.  Minimum variance capacity identification , 2007, Eur. J. Oper. Res..

[16]  Christophe Labreuche,et al.  Bi-capacities - II: the Choquet integral , 2005, Fuzzy Sets Syst..

[17]  Carlos A. Bana e Costa,et al.  On the mathematical foundations of MACBETH , 2016 .

[18]  Annie Laforet,et al.  METHODES MULTICRITERES ELECTRE. DESCRIPTION, CONSEILS PRATIQUES ET CAS D'APPLICATION A LA GESTION ENVIRONNEMENTALE , 1996 .

[19]  Salvatore Greco,et al.  Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral , 2010, Eur. J. Oper. Res..

[20]  M. Grabisch,et al.  Fuzzy Measures and Integrals in MCDA , 2004 .

[21]  Salvatore Greco,et al.  Assessing non-additive utility for multicriteria decision aid , 2004, Eur. J. Oper. Res..

[22]  Michel Grabisch,et al.  The representation of importance and interaction of features by fuzzy measures , 1996, Pattern Recognit. Lett..

[23]  Jean-Luc Marichal,et al.  Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices , 2006, Games Econ. Behav..

[24]  Bruno Dente,et al.  Understanding Policy Decisions , 2013 .

[25]  S. Greco,et al.  The bipolar Choquet integral representation , 2014 .

[26]  Ivan Kojadinovic,et al.  A weight-based approach to the measurement of the interaction among criteria in the framework of aggregation by the bipolar Choquet integral , 2007, Eur. J. Oper. Res..

[27]  Michel Grabisch,et al.  An axiomatic approach to the concept of interaction among players in cooperative games , 1999, Int. J. Game Theory.

[28]  José Rui Figueira,et al.  Discriminating thresholds as a tool to cope with imperfect knowledge in multiple criteria decision aiding: Theoretical results and practical issues , 2014 .

[29]  Valentina Ferretti,et al.  Assessing Different Possibilities for the Reuse of an Open-pit Quarry Using the Choquet Integral , 2014 .

[30]  Michel Grabisch,et al.  Set Functions, Games and Capacities in Decision Making , 2016 .

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

[32]  Valentina Ferretti,et al.  From stakeholders analysis to cognitive mapping and Multi-Attribute Value Theory: An integrated approach for policy support , 2016, Eur. J. Oper. Res..

[33]  Eleftherios Siskos,et al.  Elicitation of criteria importance weights through the Simos method: A robustness concern , 2015, Eur. J. Oper. Res..

[34]  Valentina Ferretti,et al.  Actor-Network-Theory perspective on a forestry decision support system design , 2014, DSS 2013.

[35]  W. Edwards,et al.  Decision Analysis and Behavioral Research , 1986 .