Advertisement

Intuitionistic Fuzzy Probability

  • Claudilene Gomes Da Costa
  • Benjamin Callejas Bedregal
  • Adrião Duarte Doria Neto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6404)

Abstract

Fuzzy Probabilities are an extension of the concept of probabilities with application in several practical problems. The former are probabilities represented through fuzzy numbers, to indicate the uncertainty in the value assigned to a probability. Moreover, Krassimir Atanassov in 1983 added an extra degree of uncertainty to classic fuzzy sets for modeling the hesitation and uncertainty about the degree of membership. This new theory of fuzzy sets is known today as intuitionistic fuzzy set theory.

This work will extend the notion of fuzzy probabilities by representing probabilities through the intuitionistic fuzzy numbers, in the sense of Atanassov, instead of fuzzy numbers.

Keywords

Fuzzy Number Approximate Reasoning Fuzzy Probability Intuitionistic Fuzzy Number Sport Betting 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Atanassov, K.T.: Intuitionistic Fuzzy Sets. Central Tech. Library, Bulgarian Academy Science, Sofia, Bulgaria, Rep. No. 1697/84 (1983)Google Scholar
  2. 2.
    Atanassov, K.T.: Intuitionistic Fuzzy Sets: Theory and Applications. Springer, Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  3. 3.
    Ban, A.I.: Nearest Interval Approximation of an Intuitionistic Fuzzy Number. In: Reusch, B. (ed.) Computational Intelligence, Theory and Applications, pp. 229–240. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Buchdahl, J.: Fixed Odds Sports Betting: Statistical Forecasting and Risk Management. High Stakes Publishing (2003)Google Scholar
  5. 5.
    Buckley, J.J.: Fuzzy Probabilities: A new approach and applications. Springer, Berlin (2005)zbMATHGoogle Scholar
  6. 6.
    Buckley, J.J.: Fuzzy Probabilities and Statistics. Springer, Berlin (2006)zbMATHGoogle Scholar
  7. 7.
    Burillo, P., Bustince, H., Mohedano, V.: Some definitions of intuitionistic fuzzy number. First properties. In: Lakov, D. (ed.) Proceedings of the 1st Workshop on Fuzzy Based Expert Systems, Sofia, Bulgaria, pp. 53–55 (September 1994)Google Scholar
  8. 8.
    Bustince, H., Montero, J., Orduna, R., Barrenechea, E., Pagola, M.: A survey of Atanassov’s Intuitionistic Fuzzy Relations. In: Intuitionistic Fuzzy Sets: Recent Advances. Studies in Fuzziness and Soft Computing. Springer, Heidelberg (2008)Google Scholar
  9. 9.
    Campos, M.A., Dimuro, G.P., Costa, A.C.R., Araújo, J.F., Dias, A.M.: Probabilidade Intervalar e Cadeias de Markov Intervalares no Maple. Tema – Tendências em Matemática Aplicada e Computacional 3(2), 53–62 (2002)Google Scholar
  10. 10.
    Ciungu, L.C., Riecan, B.: Representation theorem for probabilities on IFS-events. Information Sciences 180, 793–798 (2010)CrossRefzbMATHGoogle Scholar
  11. 11.
    Cornelis, C., Deschrijver, G., Kerre, E.E.: Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application. International Journal of Approximate Reasoning 35, 55–95 (2004)CrossRefzbMATHGoogle Scholar
  12. 12.
    Deschrijver, G., Kerre, E.E.: On the Relationship Between some Extensions of Fuzzy Set Theory. Fuzzy Sets and Systems 133(2), 227–235 (2003)CrossRefzbMATHGoogle Scholar
  13. 13.
    Deschrijver, G., Cornelis, C., Kerre, E.E.: Intuitionistic Fuzzy Connectives Revised. In: Proc. 9th Int. Conf. Information Processing Management Uncertainty Knowledge-based Systems, pp. 1839–1844 (2002)Google Scholar
  14. 14.
    Deschrijver, G., Cornelis, C., Kerre, E.E.: On the Representation of Intuitionistic Fuzzy t-Norms and t-Conorms. IEEE Trans. on Fuzzy Systems 12(1), 45–61 (2004)CrossRefzbMATHGoogle Scholar
  15. 15.
    Dunyak, J., Saad, L.W., Wunsch, D.: A Theory of Independent Fuzzy Probability for System Reliability. IEEE Trans. Fuzzy Systems 7, 286–294 (1999)CrossRefGoogle Scholar
  16. 16.
    Grzegorzewski, P., Mrowka, E.: Probability of intuitionistic fuzzy events. In: Grzegorzewski, P., et al. (eds.) Soft Methods in Probability, Statistics and Data Analysis, pp. 105–115. Physica-Verlag, NewYork (2002)CrossRefGoogle Scholar
  17. 17.
    Grzegorzewski, P.: Distances and orderings in a family of intuitionistic fuzzy numbers. In: Proc. of EUSFLAT Conf. 2003, pp. 223–227 (2003)Google Scholar
  18. 18.
    Goguen, J.A.: L-fuzzy sets. Journal of Mathematical Analysis and Applications 18(1), 623–668 (1967)CrossRefzbMATHGoogle Scholar
  19. 19.
    Guha, D., Chakraborty, D.: A Theoretical Development of Distance Measure for Intuitionistic Fuzzy Numbers. International Journal of Mathematics and Mathematical Sciences 2010, Article ID 949143, 25 pagesGoogle Scholar
  20. 20.
    Haigh, J.: Taking Chances: Winning with Probability. Oxford University Press, Oxford (2003)zbMATHGoogle Scholar
  21. 21.
    Hall, J.W., Blockley, D.I., Davis, J.P.: Uncertain Inference Using Interval Probability Theory. Approximate Reasoning 19, 247–264 (1998)CrossRefzbMATHGoogle Scholar
  22. 22.
    Hirotsu, N., Wright, M.: Using a Markov process model of an association football match to determine the optimal timing of substitution and tactical decisions. Journal of the Operational Research Society 53, 88–96 (2002)CrossRefzbMATHGoogle Scholar
  23. 23.
    Kolev, B., Chountas, P., Petrounias, I., Kodogiannis, V.: An Application of Intuitionistic Fuzzy Relational Databases in Football Match Result Predictions. In: Reusch, B. (ed.) Computational Intelligence, Theory and Applications, pp. 281–289. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  24. 24.
    Lee, A.J.: Modeling scores in Premier League: is Manchester United really the best. Chance 10, 15–19 (1997)CrossRefGoogle Scholar
  25. 25.
    Liu, H., Shi, K.: Intuitionistic fuzzy numbers and intuitionistic distribution numbers. Journal of Fuzzy Mathematics 8(4), 909–918 (2000)zbMATHGoogle Scholar
  26. 26.
    Pankowska, A., Wygralak, M.: Intuitionistic fuzzy sets – An alternative approach. In: EUSFLAT 2003 Proceedings, Zittau, Germany, September 10-12, pp. 135–140 (2003)Google Scholar
  27. 27.
    Reconvá, M., Riecan, B.: Observables on Intuitionistic Fuzzy Sets: An Elementary Approach. Cybernetics and Information Technologes 9(2), 38–42 (2009)Google Scholar
  28. 28.
    Nayagam, V.L.G., Venkateshwari, G., Sivaraman, G.: Ranking of intuitionistic fuzzy numbers. In: Proceedings of IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2008), Hong Kong, pp. 1971–1974 (June 2008)Google Scholar
  29. 29.
    Rue, H., Salvesen, Ø.: Prediction and retrospective analysis of soccer matches in a league. The Statistician 49(3), 399–418 (2000)Google Scholar
  30. 30.
    Takeuti, G., Titani, S.: Intuitionistic fuzzy logic and intuitionistic fuzzy set theory. Journal of Symbolic Logic 49(3), 851–866 (1984)CrossRefzbMATHGoogle Scholar
  31. 31.
    Weichselberger, K.: The Theory of Interval-Probability as a Unifying Concept for Uncertainty. Approximate Reasoning 24, 149–170 (2000)CrossRefzbMATHGoogle Scholar
  32. 32.
    Yager, R.R.: Probabilities from fuzzy observations. Information Science 32(1), 1–31 (1984)CrossRefzbMATHGoogle Scholar
  33. 33.
    Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)CrossRefzbMATHGoogle Scholar
  34. 34.
    Zadeh, L.A.: Fuzzy Probabilities. Information Processing and Management 20, 363–372 (1984)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Claudilene Gomes Da Costa
    • 1
  • Benjamin Callejas Bedregal
    • 2
  • Adrião Duarte Doria Neto
    • 3
  1. 1.Departamento de Ciências Exatas – DCEUniversidade Federal da Paraíba – UFPBRio TintoBrasil
  2. 2.Grupo de Lógica, Linguagens, Informação, Teoria e Aplicações – LoLITA, Departamento de Informática e Matemática Aplicada – DIMApUniversidade Federal do Rio Grande do Norte – UFRNNatalBrazil
  3. 3.Departamento de Engenharia de Computação e Automação – DCAUniversidade Federal do Rio Grande do Norte – UFRNNatalBrazil

Personalised recommendations