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

  • Silvia Angilella
  • Sally Giuseppe ArcidiaconoEmail author
  • Salvatore Corrente
  • Salvatore Greco
  • Benedetto Matarazzo
Original Paper

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.

Keywords

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

Notes

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”.

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):734–744CrossRefGoogle 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):277–288CrossRefGoogle 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):172–182CrossRefGoogle 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):489–500CrossRefGoogle Scholar
  5. Barron FH, Barrett BE (1996) Decision quality using ranked attribute weights. Manag Sci 42(11):1515–1523CrossRefGoogle Scholar
  6. Brans JP, Vincke Ph (1985) A preference ranking organisation method: the PROMETHEE method for MCDM. Manag Sci 31(6):647–656CrossRefGoogle 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 17:263–283CrossRefGoogle Scholar
  8. Choquet G (1953) Theory of capacities. Ann Inst Fourier 5:131–295CrossRefGoogle 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 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):6106–6113CrossRefGoogle 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):563–73Google Scholar
  12. Edwards W (1977) How to use multiattribute utility measurement for social decisionmaking. IEEE Trans Syst Man Cybern 7(5):326–340CrossRefGoogle Scholar
  13. Figueira JR, Greco S, Roy B, Słowiński R (2013) An overview of ELECTRE methods and their recent extensions. J Multicriteria Decis Anal 20:61–85CrossRefGoogle Scholar
  14. Figueira JR, Greco S, Ehrgott M (2016) Multiple criteria decision analysis: state of the art surveys. Springer, BerlinGoogle 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 507–527Google Scholar
  16. Gilboa I, Schmeidler D (1994) Additive representations of non-additive measures and the Choquet integral. Ann Oper Res 52:43–65CrossRefGoogle Scholar
  17. Grabisch M (1996) The application of fuzzy integrals in multicriteria decision making. Eur J Oper Res 89:445–456CrossRefGoogle Scholar
  18. Grabisch M (1997) \(k\)-order additive discrete fuzzy measures and their representation. Fuzzy Sets Syst 92:167–189CrossRefGoogle Scholar
  19. Greco S, Matarazzo B, Slowinski R (2001) Rough sets theory for multicriteria decision analysis. Eur J Oper Res 129(1):1–47CrossRefGoogle Scholar
  20. Hwang CL, Yoon K (1981) Multiple attribute decision making. Springer, New YorkCrossRefGoogle Scholar
  21. Ishizaka A, Nemery P (2013) Multi-criteria decision analysis: methods and software. Wiley, New YorkCrossRefGoogle Scholar
  22. Jablonsky J (2012) Multicriteria analysis of classification in athletic decathlon. Multiple Criteria Decis Mak 7:112–120Google Scholar
  23. Jacquet-Lagrèze E, Siskos Y (2001) Preference disaggregation: 20 years of MCDA experience. Eur J Oper Res 130(2):233–245CrossRefGoogle Scholar
  24. Keeney RL, Raiffa H (1993) Decisions with multiple objectives: preferences and value tradeoffs. Wiley, New YorkCrossRefGoogle Scholar
  25. Kendall G, Knust S, Ribeiro CC, Urrutia S (2010) Scheduling in sports: an annotated bibliography. Comput Oper Res 37(1):1–19CrossRefGoogle Scholar
  26. Lahdelma R, Salminen P (2001) SMAA-2: stochastic multicriteria acceptability analysis for group decision making. Oper Res 49(3):444–454CrossRefGoogle Scholar
  27. Lahdelma R, Hokkanen J, Salminen P (1998) SMAA—stochastic multiobjective acceptability analysis. Eur J Oper Res 106(1):137–143CrossRefGoogle 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):304–312Google Scholar
  29. Marichal JL, Roubens M (2000) Determination of weights of interacting criteria from a reference set. Eur J Oper Res 124(3):641–650CrossRefGoogle 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 164–171Google Scholar
  31. Mottley CM (1954) The application of operations-research methods to athletic games. J Oper Res Soc Am 2(3):335–338Google Scholar
  32. Murofushi S, Soneda T (1993) Techniques for reading fuzzy measures (III): interaction index. In: 9th fuzzy systems symposium, Sapporo, pp 693–696Google Scholar
  33. Olson DL (2001) Comparison of three multicriteria methods to predict known outcomes. Eur J Oper Res 130(3):576–587CrossRefGoogle Scholar
  34. Rota GC (1964) On the foundations of combinatorial theory. I. Theory of Möbius functions. Wahrs Verwandte Geb 2:340–368CrossRefGoogle Scholar
  35. Roy B (1996) Multicriteria methodology for decision aiding. Kluwer, DordrechtCrossRefGoogle Scholar
  36. Saaty T (1990) How to make a decision: the analytic hierarchy process. Eur J Oper Res 48(1):9–26CrossRefGoogle 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 307Google Scholar
  38. Smith RL (1984) Efficient Monte Carlo procedures for generating points uniformly distributed over bounded regions. Oper Res 32:1296–1308CrossRefGoogle 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 325–333Google Scholar
  40. Sugeno M (1974) Theory of fuzzy integrals and its applications. PhD thesis, Tokyo Institute of TechnologyGoogle Scholar
  41. Tervonen T, Figueira JR (2008) A survey on stochastic multicriteria acceptability analysis methods. J Multicriteria Decis Anal 15(1–2):1–14Google 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 224:552–559CrossRefGoogle Scholar
  43. Wright MB (2009) 50 years of OR in sport. J Oper Res Soc 60(1):S161–S168CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Silvia Angilella
    • 1
  • Sally Giuseppe Arcidiacono
    • 1
    Email author
  • Salvatore Corrente
    • 1
  • Salvatore Greco
    • 1
    • 2
  • Benedetto Matarazzo
    • 1
  1. 1.Department of Economics and BusinessUniversity of CataniaCataniaItaly
  2. 2.Centre of Operations Research and Logistics (CORL), Portsmouth Business SchoolUniversity of PortsmouthPortsmouthUK

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