Assessing the Players’ Performance in the Game of Bridge: A Fuzzy Logic Approach

Michael Gr. Voskoglou^1,

¹School of Technological Applications, Graduate Technological Educational Institute (T. E. I.) of Western Greece, Patras, Greece

Cite this paper:
Michael Gr. Voskoglou. Assessing the Players’ Performance in the Game of Bridge: A Fuzzy Logic Approach. American Journal of Applied Mathematics and Statistics. 2014; 2(3):115-120. doi: 10.12691/ajams-2-3-5

Abstract

Contract bridge occupies nowadays a position of great prestige being, together with chess, the only mind sports officially recognized by the International Olympic Committee. In the present paper an innovative method for assessing the total performance of bridge-players’ belonging to groups of special interest (e.g. different bridge clubs during a tournament, men and women, new and old players, etc) is introduced, which is based on principles of fuzzy logic. For this, the cohorts under assessment are represented as fuzzy subsets of a set of linguistic labels characterizing their performance and the centroid defuzzification method is used to convert the fuzzy data collected from the game to a crisp number. This new method of assessment could be used informally as a complement of the official bridge-scoring methods for statistical and other obvious reasons. Two real applications related to simultaneous tournaments with pre-dealt boards, organized by the Hellenic Bridge Federation, are also presented, illustrating the importance of our results in practice.

Keywords:
contract bridge fuzzy sets centroid defuzzification method

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References:

[1]	“Bridge Base Online (BBO)”, available on the Web at www.bridgebase.com/index.php?d=y
[2]	“Bridge rules and variations”, available on the Web at www.pagat.com/boston/bridge.html.
[3]	“Contract bridge”, available on the Web at http://en.wikipedia.org/wiki/contract_bridge
[4]	D’ Orsi, E. (chair) et al., “The New WBF IMP to VP Scales”, Technical Report of WBF Scoring Panel, available on the Web at www.worldbridge.org/Data/Sites/1/media/documents/regulations/WBFAlgorithms.pdf
[5]	“Hellas Bridge Federation” (in Greek), available on the Web at www.hellasbridge.org
[6]	Kaplan, E., Winning Contract Bridge Complete, Fleet Publishing Corporation, N. Y., 1964.
[7]	Kaplan, E., Winning Contract Bridge, Courier Dover Publications, N. Y., 2010.
[8]	Klir, G. J. & Folger, T. A.., Fuzzy Sets, Uncertainty and Information, Prentice-Hall, London, 1988.
[9]	Subbotin, I. Ya. Badkoobehi, H. & Bilotckii, N. N.., “Application of fuzzy logic to learning assessment”, Didactics of Mathematics: Problems and Investigations, 22, 38-41, 2004.
[10]	Voskoglou, M. Gr., “The process of learning mathematics: A fuzzy set approach”, Heuristic and Didactics of Exact Sciences,, 10, 9-13, 1999.
[11]	Voskoglou, M. Gr., “Fuzzy Sets in Case-Based Reasoning”, Fuzzy Systems and Knowledge Discovery, IEEE Computer Society, Vol. 6, 252-256, 2009.
[12]	Voskoglou, M. Gr., Stochastic and fuzzy models in Mathematics Education, Artificial Intelligence and Management, Lambert Academic Publishing, Saarbrucken, Germany, 2011.
[13]	Voskoglou, M. Gr., “Fuzzy Logic and Uncertainty in Mathematics Education”, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, 1, 45-64, 2011.
[14]	Voskoglou, M. Gr. & Subbotin, I. Ya., “Fuzzy Models for Analogical Reasoning”, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, 2, 19-38, 2012.
[15]	Voskoglou, M. Gr., “A study on fuzzy systems”, American Journal of Computational and Applied Mathematics, 2 (5), 232-240, 2012.
[16]	Voskoglou, M. Gr., “Assessing Students’ Individual Problem Solving Skills”, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, 3, 39-49, 2013.
[17]	Voskoglou, M. Gr & Subbotin, I. Ya,, “Dealing with the Fuzziness of Human Reasoning”, International Journal of Applications of Fuzzy Sets and Artificial Intelligence, 3, 91-106, 2013.
[18]	Voskoglou, M. Gr, “Fuzzy Logic in the APOS/ACE Instructional Treatment for Mathematics”, American Journal of Applied Mathematics and Statistics, 2014.
[19]	Zadeh, L. A., “Fuzzy Sets”, Information and Control, 8, 338- 353, 1965.