Non Additive Robust Ordinal Regression for urban and territorial planning: an application for siting an urban waste landfill

Abstract

In this paper we deal with an urban and territorial planning problem by applying the Non Additive Robust Ordinal Regression (NAROR). NAROR is a recent extension of the Robust Ordinal Regression family of Multiple Criteria Decision Aiding methods to the Choquet integral preference model which permits to represent interaction between considered criteria through the use of a set of non-additive weights called capacity or fuzzy measure. The use of NAROR permits the Decision Maker (DM) to give preference information in terms of preferences between pairs of alternatives with which she is familiar, and relative importance and interaction of considered criteria. The basic idea of NAROR is to consider the whole set of capacities that are compatible with the preference information given by the DM. In fact, the recommendation supplied by NAROR is expressed in terms of necessary preferences, in case an alternative is preferred to another for all compatible capacities, and of possible preferences, in case an alternative is preferred to another for at least one compatible capacity. In the considered case study, several sites for the location of a landfill are analyzed and compared through the use of the NAROR on the basis of different criteria, such as presence of population, hydrogeological risk, interferences on transport infrastructures and economic cost. This paper is the first application of NAROR to a real-world problem, even if not already with real DMs, but with a panel of experts simulating the decision process.

This is a preview of subscription content, access via your institution.

Fig. 1

References

  1. 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(1), 172–182.

  2. Angilella, S., Corrente, S., Greco, S., & Słowiński, R. (2013). Multiple criteria hierarchy process for the Choquet integral. In R. Purshouse et al. (Eds.) Proceedings of EMO 2013, EMO 2013. LNCS 7811, pp. 475–489.

  3. 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.

    Article  Google Scholar 

  4. Angilella, S., Greco, S., & Matarazzo, B. (2010a). Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral. European Journal of Operational Research, 201(1), 277–288.

    Article  Google Scholar 

  5. Angilella, S., Greco, S., & Matarazzo, B. (2010b). The most representative utility function for non-additive robust ordinal regression. In E. Hullermeier, R. Kruse, and F. Hoffmann (Eds.) Proceedings of IPMU 2010, IPMU 2010 (pp. 220–257), LNAI 6178. Springer, Heidelberg.

  6. ATO-R (Associazione d’Ambito Torinese per il Governo dei Rifiuti) (2007). Discarica per rifiuti non pericolosi del pinerolese. http://www.atorifiutitorinese.it/index.php?option=com_content&task=view&id=80&Itemid=96

  7. Bobbio, L. (2011). Conflitti territoriali: sei interpretazioni. Tema, 4(4), 79–88.

    Google Scholar 

  8. Bottero, M., Ferretti, V., & Mondini, G. (2013). A Choquet integral—based approach for assessing the sustainability of a new waste incinerator. International Journal of Multicriteria Decision Making, 3(2/3), 157–177.

    Article  Google Scholar 

  9. Brans, J. P., & Vincke, Ph. (1985). A preference ranking organisation method: The PROMETHEE method for MCDM. Management Science, 31(6), 647–656.

    Article  Google Scholar 

  10. Chateauneuf, A., & Jaffray, J. Y. (1989). Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion. Mathematical Social Sciences, 17, 263–283.

    Article  Google Scholar 

  11. Choquet, G. (1953). Theory of capacities. Annales Institute Fourier, 5(54), 131–295.

    Google Scholar 

  12. Corrente, S., Figueira, J. R., & Greco, S. (2014a). Dealing with interaction between bipolar multiple criteria preferences in PROMETHEE method. Annals of Operations Research, 217(1), 137–164.

    Article  Google Scholar 

  13. Corrente, S., Greco, S., & Słowiński, R. (2012). Multiple criteria hierarchy process in robust ordinal regression. Decision Support Systems, 53(3), 660–674.

    Article  Google Scholar 

  14. Corrente, S., Greco, S., & Słowiński, R. (2013a). Multiple criteria hierarchy process with ELECTRE and PROMETHEE. Omega, 41(5), 820–846.

    Article  Google Scholar 

  15. Corrente, S., Greco, S., Kadziński, M., & Słowiński, R. (2013b). Robust ordinal regression in preference learning and ranking. Machine Learning, 93(2–3), 381–422.

    Article  Google Scholar 

  16. Corrente, S., Greco, S., Kadziński, M., Słowiński, R. (2014b). Robust ordinal regression. Wiley Encycolpedia of Operations Research and Management Science, 1–10.

  17. Dente, B. (2014). Understanding policy decisions. Berlin: Springer.

    Book  Google Scholar 

  18. Ferretti, V., & Pomarico, S. (2013). Ecological land suitability analysis through spatial indicators: An application of the Analytic Network Process technique and Ordered Weighted Average approach. Ecological Indicators, 34, 507–519.

    Article  Google Scholar 

  19. Figueira, J. R., Greco, S., & Ehrgott, M. (Eds.). (2005). Multiple criteria decision analysis: State of the art surveys. Berlin: Springer.

    Google Scholar 

  20. 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, 478–495.

    Article  Google Scholar 

  21. Figueira, J. R., Greco, S., & Słowiński, R. (2010). Building a set of additive value functions representing a reference preorder and intensities of preference: GRIP method. European Journal of Operational Research, 195(2), 460–486.

    Article  Google Scholar 

  22. Figueira, J. R., Greco, S., & Słowiński, R. (2008). Identifying the “most representative” value function among all compatible value functions in the GRIP. In Proceedings of the 68th EURO Working Group on MCDA, Chania, October 2008.

  23. Foster, S. S. D. (1987). Fundamental concepts in aquifer vulnerability, pollution risk and protection strategy. In W. van Duijvenbooden, & H. G. van Waegeningh (Eds.) TNO Committee on Hydrological Research, The Hague. Vulnerability of soil and ground- water to pollutants, Proceedings and Information, vol. 38, pp. 69–86.

  24. Giove, S., Rosato, P., & Breil, M. (2011). An application of multicriteria decision making to built heritage. The redevelopment of Venice Arsenale. Journal of Multi-Criteria Decision Analysis, 17(3–4), 85–99.

    Google Scholar 

  25. Glasson, J., Therivel, R., & Chadwick, A. (2013). Introduction to environmental impact assessment. London: Routledge.

    Google Scholar 

  26. Grabisch, M. (1996). The application of fuzzy integrals in multicriteria decision making. European Journal of Operational Research, 89(3), 445–456.

    Article  Google Scholar 

  27. Grabisch, M. (1997). k-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems, 92, 167–189.

    Article  Google Scholar 

  28. Grabisch, M., & Labreuche, C. (2010). A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. Annals of Operations Research, 175(1), 247–286.

    Article  Google Scholar 

  29. 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.

    Article  Google Scholar 

  30. Greco, S., Kadziński, M., Mousseau, V., & Sł owiński, R. (2011a). ELECTRE\(^{{\rm GKMS}}\): Robust ordinal regression for outranking methods. European Journal of Operational Research, 214(1), 118–135.

    Article  Google Scholar 

  31. Greco, S., Kadziński, M., Mousseau, V., & Słowiński, R. (2012). Robust ordinal regression for multiple criteria group decision: UTA\(^{{\rm GMS}}\)-GROUP and UTADIS\(^{GMS}\)-GROUP. Decision Support Systems, 52, 549–561.

    Article  Google Scholar 

  32. Greco, S., Kadziński, M., & Słowiński, R. (2011b). Selection of a representative value function in robust multiple criteria sorting. Computers & Operations Research, 38, 1620–1637.

    Article  Google Scholar 

  33. Greco, S., Matarazzo, B., & Słowiński, R. (2001). Rough sets theory for multicriteria decision analysis. European Journal of Operational Research, 129(1), 1–47.

    Article  Google Scholar 

  34. Greco, S., Mousseau, V., & Słowiński, R. (2008). Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions. European Journal of Operational Research, 191(2), 416–436.

    Article  Google Scholar 

  35. Greco, S., Mousseau, V., & Słowiński, R. (2014). Robust ordinal regression for value functions handling interacting criteria. European Journal of Operational Research, 239(3), 711–730.

  36. Kadziński, M., Greco, S., & Słowiński, R. (2011). Selection of a representative value function in robust multiple criteria ranking and choice. European Journal of Operational Research, 217(3), 541–553.

    Article  Google Scholar 

  37. Kadziński, M., Greco, S., & Słowiński, R. (2012a). Extreme ranking analysis in robust ordinal regression. Omega, 40(4), 488–501.

    Article  Google Scholar 

  38. Kadziński, M., Greco, S., & Słowiński, R. (2012b). Selection of a representative set of parameters for robust ordinal regression outranking methods. Computers & Operations Research, 39(11), 2500–2519.

    Article  Google Scholar 

  39. Kadziński, M., Greco, S., & Słowiński, R. (2013). Selection of a representative value function for robust ordinal regression in group decision making. Group Decision and Negotiation, 22(3), 429–462.

    Article  Google Scholar 

  40. Kadziński, M., & Tervonen, T. (2013). Robust multi-criteria ranking with additive value models and holistic pair-wise preference statements. European Journal of Operational Research, 228(1), 169–180.

    Article  Google Scholar 

  41. Keeney, R. L., & Raiffa, H. (1993). Decisions with multiple objectives: Preferences and value tradeoffs. New York: Wiley.

    Book  Google Scholar 

  42. Lahdelma, R., Hokkanen, J., & Salminen, P. (1998). SMAA-Stochastic multiobjective acceptability analysis. European Journal of Operational Research, 106, 137–143.

    Article  Google Scholar 

  43. Malczewski, J. (1999). GIS and multicriteria decision analysis. New York: Wiley.

    Google Scholar 

  44. 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.

    Article  Google Scholar 

  45. Mousseau, V., Figueira, J. R., Dias, L., Gomes da Silva, C., & Climaco, J. (2003). Resolving inconsistencies among constraints on the parameters of an MCDA model. European Journal of Operational Research, 147(1), 72–93.

    Article  Google Scholar 

  46. Munda, G. (2005). Social multi-criteria evaluation for urban sustainability policies. Land Use Policy, 23(1), 86–94.

    Article  Google Scholar 

  47. Murofushi, S., & Soneda, T. (1993). Techniques for reading fuzzy measures (III): Interaction index. In 9th fuzzy systems symposium, Sapporo, Japan, pp. 693–696.

  48. Rosenhead, J., & Mingers, J. (Eds.). (2001). Rational analysis for a problematic word Revised. Chichester: Wiley.

    Google Scholar 

  49. Rota, G. C. (1964). On the foundations of combinatorial theory I. Theory of Möbius functions. Wahrscheinlichkeitstheorie und Verwandte Gebiete, 2, 340–368.

    Article  Google Scholar 

  50. Roy, B., & Bouyssou, D. (1993). Aide multicritère à la décision: méthodes et cas. Paris: Economica.

    Google Scholar 

  51. Roy, B., & Słowiński, R. (2013). Questions guiding the choice of a multicriteria decision aiding method. EURO Journal on Decision Process, 1, 69–97.

    Article  Google Scholar 

  52. Singh, R. S., Murty, H. R., Gupta, S. K., & Dikshit, A. K. (2012). An overview of sustainability assessment methodologies. Ecologial Indicators, 15, 281–299.

    Article  Google Scholar 

  53. Shafer, G. (1976). A mathematical theory of evidence. Princeton: Princeton University Press.

    Google Scholar 

  54. Shapley, L. S. (1953). A value for n-person games. In A. W. Tucker & H. W. Kuhn (Eds.), Contributions to the theory of games II. Princeton: Princeton University Press.

    Google Scholar 

  55. Tervonen, T., & Figueira, J. R. (2008). A survey on stochastic multicriteria acceptability analysis methods. Journal of Multi-Criteria Decision Analysis, 15(1–2), 1–14.

    Article  Google Scholar 

  56. Wakker, P. P. (1989). Additive representations of preferences: A new foundation of decision analysis. Dordrecht: Kluwer Academic Publishers.

    Book  Google Scholar 

Download references

Acknowledgments

The third and the fifth authors wishe to acknowledge funding by the Programma Operativo Nazionale, Ricerca & Competitività 2007-2013 within the project PON04a2 E SINERGREEN-RES-NOVAE.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Marta Bottero.

Appendices

Appendix 1: Rank acceptability indices

Table 13 Cumulative rank acceptability indices \(b^{k}_{\le l}\) for all 39 considered sites and for \(l=1,{\ldots },5\)
Table 14 Cumulative rank acceptability indices \(b^{k}_{\ge l}\) for all 39 considered sites and for \(l=35,{\ldots },39\)

Appendix 2: Necessary preference relation

Table 15 Necessary preference relation obtained by applying the NAROR

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Angilella, S., Bottero, M., Corrente, S. et al. Non Additive Robust Ordinal Regression for urban and territorial planning: an application for siting an urban waste landfill. Ann Oper Res 245, 427–456 (2016). https://doi.org/10.1007/s10479-015-1787-7

Download citation

Keywords

  • Urban and territorial planning
  • Choquet integral
  • Indirect preference information
  • NAROR