How to cite this paper
Dolgun, L., Burnak, N & Koksal, G. (2020). Representing preferences by Choquet integral: Guidelines to specify the capacity type.Decision Science Letters , 9(3), 387-408.
Refrences
Abdullah, L., Zulkifli, N., Liao, H., Herrera-Viedma, E., & Al-Barakati, A. (2019). An interval-valued intuitionistic fuzzy DEMATEL method combined with Choquet integral for sustainable solid waste management. Engineering Applications of Artificial Intelligence, 82, 207-215.
Angilella, S., Corrente, S., & Greco, S. (2015). Stochastic multiobjective acceptability analysis for the Choquet integral preference model and the scale construction problem. European Journal of Operational Research, 240, 172–182.
Angilella, S., Corrente, S., Greco, S., & Słowiński, R. (2013, March). Multiple criteria hierarchy process for the Choquet integral. In Proceedings of International Conference on Evolutionary Multi-Criterion Optimization (pp. 475-489). Springer, Berlin, Heidelberg.
Angilella, S., Greco, S., Lamantia, F., & Matarazzo B. (2004). Assessing non-additive utility for multicriteria decision aid. European Journal of Operational Research, 158(3), 734–744.
Angilella, S., Greco, S., & Matarazzo, B. (2010). Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral. European Journal of Operational Research, 201(1), 277–288.
Bottero, M., Ferretti, V., Figueira, J.R., Greco, S., & Roy, B. (2018). On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application. European Journal of Operational Research, 271(1), 120-140.
Choquet, G. (1953). Theory of capacities. Annales de l’Institut Fourier, 5, 131–295.
Corrente, S., Figueira, J.R., & Greco, S. (2014). Dealing with interaction between bipolar multiple criteria preferences in PROMETHEE methods. Annals of Operations Research, 217(1), 137–164.
Doumpos, M., & Zopounidis, C. (2011). Preference disaggregation and statistical learning for multicriteria decision support: A review. European Journal of Operational Research, 209, 203-214.
Dyer, J. S. (2005). MAUT—multiattribute utility theory. In Figueira, J.R., Greco, S., Ehrgott, M. (Eds.), Multiple criteria decision analysis: state of the art surveys (pp. 265-295). Springer, New York, NY.
Figueira, J.R., Greco, S. & Roy, B. (2009). ELECTRE methods with interaction between criteria: An extension of the concordance index. European Journal of Operational Research, 199(2), 478–495.
Grabisch, M. (2004, July). The Choquet integral as a linear interpolator. In Proceedings of 10th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2004) (pp. 373-378).
Grabisch, M., Kojadinovic, I., & Meyer, P. (2008). A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package. European Journal of Operational Research, 186(2), 766–785.
Grabisch, M., & Labreuche, C. (2003, September). Capacities on lattices and k-ary capacities. In Proceedings of EUSFLAT Conf. (pp. 304-307). Zittau, Germany.
Grabisch, M., & Labreuche, C. (2005a). Fuzzy measures and integrals in MCDA. In Figueira, J.R., Greco, S., Ehrgott, M. (Eds.), Multiple criteria decision analysis: state of the art surveys (pp. 563-604). Springer, New York, NY.
Grabisch, M., & Labreuche, C. (2005b). Bi-capacities—I: definition, Möbius transform and interaction. Fuzzy Sets and Systems, 151, 211–236.
Grabisch, M., & Labreuche, C. (2005c). Bi-capacities—II: the Choquet integral. Fuzzy Sets and Systems, 151, 237–259.
Grabisch, M., & Labreuche, C. (2008a). A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. 4OR, 6(1), 1–44.
Grabisch, M., & Labreuche, C. (2008b). Bipolarization of posets and natural interpolation. Journal of Mathematical Analysis and Applications, 343, 1080-1097.
Gurbuz, T., & Albayrak, Y.E. (2014). An engineering approach to human resources performance evaluation: Hybrid MCDM application with interactions. Applied Soft Computing, 21, 365-375.
Gurbuz, T., Alptekin, S.E., & Isiklar Alptekin, G. (2012). A hybrid MCDM methodology for ERP selection problem with interacting criteria. Decision Support Systems, 54, 206-214.
Ko, Y.H., Kim, K.J., & Jun, C.H. (2005) A new loss function-based method for multiresponse optimization. Journal of Quality Technology, 37(1), 50-59.
Labreuche, C., & Grabisch, M. (2007). The representation of conditional importance between criteria. Annals of Operations Research, 154, 93-122.
Lovász, L. (1983). Submodular functions and convexity. In Bachem, A., Grötschel, M., Korte, B. (Eds.), Mathematical Programming: The State of the Art (pp. 235-257). Springer, Berlin, Heidelberg.
Marichal, J.L. (2002). Aggregation of interacting criteria by means of the discrete Choquet integral. In Calvo, T., Mayor, G., Mesiar, R. (Eds.), Aggregation operators: New Trends and Applications (pp. 224-244). Physica, Heidelberg.
Marichal, J.L., & Roubens, M. (2000). Determination of weights of interacting criteria from a reference set. European Journal of Operational Research, 124(3), 641–650.
Ming-Lang, T., Chiang, J.H., & Lan, L.W. (2009). Selection of optimal supplier in supply chain management strategy with analytic network process and Choquet integral. Computers & Industrial Engineering, 57, 330-340.
Montgomery, D.C. (2005). Design and Analysis of Experiments. John Wiley and Sons, Inc.
Sicilia, M.Á., Barriocanal, E.G., & Calvo, T. (2003). An inquiry-based method for Choquet integral-based aggregation of interface usability parameters. Kybernetika, 39(5), 601-614.
Sugeno, M. (1974). Theory of fuzzy integrals and its applications. Doct. Thesis, Tokyo Institute of technology.
Timonin, M. (2013). Robust optimization of the Choquet integral. Fuzzy Sets and Systems, 213, 27-46.
Wang, L., Wang, H., Xu, Z., & Ren, Z. (2019). The interval‐valued hesitant Pythagorean fuzzy set and its applications with extended TOPSIS and Choquet integral‐based method. International Journal of Intelligent Systems, 34(6), 1063-1085.
Angilella, S., Corrente, S., & Greco, S. (2015). Stochastic multiobjective acceptability analysis for the Choquet integral preference model and the scale construction problem. European Journal of Operational Research, 240, 172–182.
Angilella, S., Corrente, S., Greco, S., & Słowiński, R. (2013, March). Multiple criteria hierarchy process for the Choquet integral. In Proceedings of International Conference on Evolutionary Multi-Criterion Optimization (pp. 475-489). Springer, Berlin, Heidelberg.
Angilella, S., Greco, S., Lamantia, F., & Matarazzo B. (2004). Assessing non-additive utility for multicriteria decision aid. European Journal of Operational Research, 158(3), 734–744.
Angilella, S., Greco, S., & Matarazzo, B. (2010). Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral. European Journal of Operational Research, 201(1), 277–288.
Bottero, M., Ferretti, V., Figueira, J.R., Greco, S., & Roy, B. (2018). On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application. European Journal of Operational Research, 271(1), 120-140.
Choquet, G. (1953). Theory of capacities. Annales de l’Institut Fourier, 5, 131–295.
Corrente, S., Figueira, J.R., & Greco, S. (2014). Dealing with interaction between bipolar multiple criteria preferences in PROMETHEE methods. Annals of Operations Research, 217(1), 137–164.
Doumpos, M., & Zopounidis, C. (2011). Preference disaggregation and statistical learning for multicriteria decision support: A review. European Journal of Operational Research, 209, 203-214.
Dyer, J. S. (2005). MAUT—multiattribute utility theory. In Figueira, J.R., Greco, S., Ehrgott, M. (Eds.), Multiple criteria decision analysis: state of the art surveys (pp. 265-295). Springer, New York, NY.
Figueira, J.R., Greco, S. & Roy, B. (2009). ELECTRE methods with interaction between criteria: An extension of the concordance index. European Journal of Operational Research, 199(2), 478–495.
Grabisch, M. (2004, July). The Choquet integral as a linear interpolator. In Proceedings of 10th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2004) (pp. 373-378).
Grabisch, M., Kojadinovic, I., & Meyer, P. (2008). A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package. European Journal of Operational Research, 186(2), 766–785.
Grabisch, M., & Labreuche, C. (2003, September). Capacities on lattices and k-ary capacities. In Proceedings of EUSFLAT Conf. (pp. 304-307). Zittau, Germany.
Grabisch, M., & Labreuche, C. (2005a). Fuzzy measures and integrals in MCDA. In Figueira, J.R., Greco, S., Ehrgott, M. (Eds.), Multiple criteria decision analysis: state of the art surveys (pp. 563-604). Springer, New York, NY.
Grabisch, M., & Labreuche, C. (2005b). Bi-capacities—I: definition, Möbius transform and interaction. Fuzzy Sets and Systems, 151, 211–236.
Grabisch, M., & Labreuche, C. (2005c). Bi-capacities—II: the Choquet integral. Fuzzy Sets and Systems, 151, 237–259.
Grabisch, M., & Labreuche, C. (2008a). A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. 4OR, 6(1), 1–44.
Grabisch, M., & Labreuche, C. (2008b). Bipolarization of posets and natural interpolation. Journal of Mathematical Analysis and Applications, 343, 1080-1097.
Gurbuz, T., & Albayrak, Y.E. (2014). An engineering approach to human resources performance evaluation: Hybrid MCDM application with interactions. Applied Soft Computing, 21, 365-375.
Gurbuz, T., Alptekin, S.E., & Isiklar Alptekin, G. (2012). A hybrid MCDM methodology for ERP selection problem with interacting criteria. Decision Support Systems, 54, 206-214.
Ko, Y.H., Kim, K.J., & Jun, C.H. (2005) A new loss function-based method for multiresponse optimization. Journal of Quality Technology, 37(1), 50-59.
Labreuche, C., & Grabisch, M. (2007). The representation of conditional importance between criteria. Annals of Operations Research, 154, 93-122.
Lovász, L. (1983). Submodular functions and convexity. In Bachem, A., Grötschel, M., Korte, B. (Eds.), Mathematical Programming: The State of the Art (pp. 235-257). Springer, Berlin, Heidelberg.
Marichal, J.L. (2002). Aggregation of interacting criteria by means of the discrete Choquet integral. In Calvo, T., Mayor, G., Mesiar, R. (Eds.), Aggregation operators: New Trends and Applications (pp. 224-244). Physica, Heidelberg.
Marichal, J.L., & Roubens, M. (2000). Determination of weights of interacting criteria from a reference set. European Journal of Operational Research, 124(3), 641–650.
Ming-Lang, T., Chiang, J.H., & Lan, L.W. (2009). Selection of optimal supplier in supply chain management strategy with analytic network process and Choquet integral. Computers & Industrial Engineering, 57, 330-340.
Montgomery, D.C. (2005). Design and Analysis of Experiments. John Wiley and Sons, Inc.
Sicilia, M.Á., Barriocanal, E.G., & Calvo, T. (2003). An inquiry-based method for Choquet integral-based aggregation of interface usability parameters. Kybernetika, 39(5), 601-614.
Sugeno, M. (1974). Theory of fuzzy integrals and its applications. Doct. Thesis, Tokyo Institute of technology.
Timonin, M. (2013). Robust optimization of the Choquet integral. Fuzzy Sets and Systems, 213, 27-46.
Wang, L., Wang, H., Xu, Z., & Ren, Z. (2019). The interval‐valued hesitant Pythagorean fuzzy set and its applications with extended TOPSIS and Choquet integral‐based method. International Journal of Intelligent Systems, 34(6), 1063-1085.