An application of the SMAA–Choquet method to evaluate the performance of sailboats in offshore regattas

Abstract

In this paper we apply a recently introduced multiple criteria decision aiding method, namely the SMAA–Choquet method, to compare the performances of different sailboats in regattas. In sailing races where sailboats with different design can participate, the performances of the boats can be evaluated by using different scoring options. In each scoring option, a corrected time is computed taking into account the physical characteristics and the performances of the sailboats. While, in real competitions, the final ranking of the sailboats is obtained by using only one of the considered scoring options, in this paper we propose to aggregate the time values computed by these scoring options in a unique one. Since the time values computed by the scoring options are given on different scales and a certain degree of interaction between them could be observed, we apply the SMAA–Choquet method that is able to deal with both aspects simultaneously.

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

Fig. 1

Notes

  1. 1.

    Supposing that all criteria have an increasing direction of preference, \(a_h\) dominates \(a_k\) if \(g_i(a_h)\ge g_i(a_k)\) for all \(i=1,\ldots ,n\), and there exists at least one \(i\in \{1,\ldots ,n\}\) such that \(g_i(a_h)>g_i(a_k)\).

  2. 2.

    Official website of the ORC: http://www.orc.org.

  3. 3.

    Official website of the Syracuse–Malta regatta: http://www.rmyc.org/races/archive/?id=115&page=4.

  4. 4.

    http://offshoreracingrule.org/.

  5. 5.

    https://www.rorcrating.com/.

  6. 6.

    http://www.ussailing.org/racing/offshore-big.

  7. 7.

    http://www.orc.org/rules/ORC%20Rating%20Systems%202015.pdf

  8. 8.

    Official website of the Syracuse–Malta regatta: http://www.rmyc.org/races/archive/?id=115&page=4.

  9. 9.

    The Performance Line is a linearization of the Performance Curve which is a function that, given the wind speed, gives back the speed of the sailboat.

References

  1. Angilella S, Greco S, Lamantia F, Matarazzo B (2004) Assessing non-additive utility for multicriteria decision aid. Eur J Oper Res 158(3):734–744

    Google Scholar 

  2. Angilella S, Greco S, Matarazzo B (2010) Non-additive robust ordinal regression: a multiple criteria decision model based on the Choquet integral. Eur J Oper Res 201(1):277–288

    Google Scholar 

  3. Angilella S, Corrente S, Greco S (2015) Stochastic multiobjective acceptability analysis for the Choquet integral preference model and the scale construction problem. Eur J Oper Res 240(1):172–182

    Google Scholar 

  4. Bana e Costa C, Vansnick J-C (1994) MACBETH—an interactive path towards the construction of cardinal value functions. Int Trans Oper Res 1(4):489–500

    Google Scholar 

  5. Barron FH, Barrett BE (1996) Decision quality using ranked attribute weights. Manag Sci 42(11):1515–1523

    Google Scholar 

  6. Brans JP, Vincke Ph (1985) A preference ranking organisation method: the PROMETHEE method for MCDM. Manag Sci 31(6):647–656

    Google Scholar 

  7. Chateauneuf A, Jaffray JY (1989) Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion. Math Soc Sci 17:263–283

    Google Scholar 

  8. Choquet G (1953) Theory of capacities. Ann Inst Fourier 5:131–295

    Google Scholar 

  9. Corrente S, Greco S, Ishizaka A (2016) Analytical hierarchy process and Choquet integral within non-additive robust ordinal regression. Omega. doi:10.1016/j.omega.2015.07.003

    Article  Google Scholar 

  10. Dadelo S, Turskis Z, Zavadskas EK, Dadeliene R (2014) Multi-criteria assessment and ranking system of sport team formation based on objective-measured values of criteria set. Expert Syst Appl 41(14):6106–6113

    Google Scholar 

  11. Dey PK, Ghosh DN, Mondal AC (2011) A MCDM approach for evaluating bowlers performance in IPL. J Emerg Trends Comput Inf Sci 2(11):563–73

    Google Scholar 

  12. Edwards W (1977) How to use multiattribute utility measurement for social decisionmaking. IEEE Trans Syst Man Cybern 7(5):326–340

    Google Scholar 

  13. Figueira JR, Greco S, Roy B, Słowiński R (2013) An overview of ELECTRE methods and their recent extensions. J Multicriteria Decis Anal 20:61–85

    Google Scholar 

  14. Figueira JR, Greco S, Ehrgott M (2016) Multiple criteria decision analysis: state of the art surveys. Springer, Berlin

    Google Scholar 

  15. Gerchak Y (1994) Operations research in sports. In: Pollock SM, Rothkopf MH, Barnett A (eds) Handbooks in operations research and management science, vol 6. Elsevier, Netherlands, pp 507–527

  16. Gilboa I, Schmeidler D (1994) Additive representations of non-additive measures and the Choquet integral. Ann Oper Res 52:43–65

    Google Scholar 

  17. Grabisch M (1996) The application of fuzzy integrals in multicriteria decision making. Eur J Oper Res 89:445–456

    Google Scholar 

  18. Grabisch M (1997) \(k\)-order additive discrete fuzzy measures and their representation. Fuzzy Sets Syst 92:167–189

    Google Scholar 

  19. Greco S, Matarazzo B, Slowinski R (2001) Rough sets theory for multicriteria decision analysis. Eur J Oper Res 129(1):1–47

    Google Scholar 

  20. Hwang CL, Yoon K (1981) Multiple attribute decision making. Springer, New York

    Google Scholar 

  21. Ishizaka A, Nemery P (2013) Multi-criteria decision analysis: methods and software. Wiley, New York

    Google Scholar 

  22. Jablonsky J (2012) Multicriteria analysis of classification in athletic decathlon. Multiple Criteria Decis Mak 7:112–120

    Google Scholar 

  23. Jacquet-Lagrèze E, Siskos Y (2001) Preference disaggregation: 20 years of MCDA experience. Eur J Oper Res 130(2):233–245

    Google Scholar 

  24. Keeney RL, Raiffa H (1993) Decisions with multiple objectives: preferences and value tradeoffs. Wiley, New York

    Google Scholar 

  25. Kendall G, Knust S, Ribeiro CC, Urrutia S (2010) Scheduling in sports: an annotated bibliography. Comput Oper Res 37(1):1–19

    Google Scholar 

  26. Lahdelma R, Salminen P (2001) SMAA-2: stochastic multicriteria acceptability analysis for group decision making. Oper Res 49(3):444–454

    Google Scholar 

  27. Lahdelma R, Hokkanen J, Salminen P (1998) SMAA—stochastic multiobjective acceptability analysis. Eur J Oper Res 106(1):137–143

    Google Scholar 

  28. Leskinen P, Viitanen J, Kangas A, Kangas J (2006) Alternatives to incorporate uncertainty and risk attitude in multicriteria evaluation of forest plans. For Sci 52(3):304–312

    Google Scholar 

  29. Marichal JL, Roubens M (2000) Determination of weights of interacting criteria from a reference set. Eur J Oper Res 124(3):641–650

    Google Scholar 

  30. Modave F, Grabisch M (1998) Preference representation by the Choquet integral: the commensurability hypothesis. In: Proceedings of the 7th international conference IPMU Paris, July 610, pp 164–171

  31. Mottley CM (1954) The application of operations-research methods to athletic games. J Oper Res Soc Am 2(3):335–338

    Google Scholar 

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

  33. Olson DL (2001) Comparison of three multicriteria methods to predict known outcomes. Eur J Oper Res 130(3):576–587

    Google Scholar 

  34. Rota GC (1964) On the foundations of combinatorial theory. I. Theory of Möbius functions. Wahrs Verwandte Geb 2:340–368

    Google Scholar 

  35. Roy B (1996) Multicriteria methodology for decision aiding. Kluwer, Dordrecht

    Google Scholar 

  36. Saaty T (1990) How to make a decision: the analytic hierarchy process. Eur J Oper Res 48(1):9–26

    Google Scholar 

  37. Shapley LS (1953) A value for n-person games. In: Tucker AW, Kuhn HW (eds) Contributions to the theory of games II. Princeton University Press, Princeton, p 307

    Google Scholar 

  38. Smith RL (1984) Efficient Monte Carlo procedures for generating points uniformly distributed over bounded regions. Oper Res 32:1296–1308

    Google Scholar 

  39. Soares de Mello JCCB, Benício J, Bragança L, Guimarães V (2013) The MACBETH method for ranking olympic sports: a complementary analysis for the DEA efficiency. In: Proceedings of the 4th international conference on mathematics in sport, Leuven, June 5–7, 2013, pp 325–333

  40. Sugeno M (1974) Theory of fuzzy integrals and its applications. PhD thesis, Tokyo Institute of Technology

  41. Tervonen T, Figueira JR (2008) A survey on stochastic multicriteria acceptability analysis methods. J Multicriteria Decis Anal 15(1–2):1–14

    Google Scholar 

  42. Tervonen T, Van Valkenhoef G, Bastürk N, Postmus D (2013) Hit-and-run enables efficient weight generation for simulation-based multiple criteria decision analysis. Eur J Oper Res 224:552–559

    Google Scholar 

  43. Wright MB (2009) 50 years of OR in sport. J Oper Res Soc 60(1):S161–S168

    Google Scholar 

Download references

Acknowledgements

The first, the third and the fourth authors wish also to acknowledge funding by the “FIR of the University of Catania BCAEA3 New developments in Multiple Criteria Decision Aiding (MCDA) and their application to territorial competitiveness”.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Sally Giuseppe Arcidiacono.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Angilella, S., Arcidiacono, S.G., Corrente, S. et al. An application of the SMAA–Choquet method to evaluate the performance of sailboats in offshore regattas. Oper Res Int J 20, 771–793 (2020). https://doi.org/10.1007/s12351-017-0340-7

Download citation

Keywords

  • Multiple criteria decision aiding
  • Decision support systems
  • Sports
  • Interacting criteria
  • Choquet integral