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Fuzzy Dominance Based on Credibility Distributions

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Fuzzy Systems and Knowledge Discovery (FSKD 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3613))

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Abstract

Comparison of fuzzy variables is considered one of the most important and interesting topics in fuzzy theory and applications. This paper introduces the new concept of fuzzy dominance based on credibility distributions of fuzzy variables. Some basic properties of fuzzy dominance are investigated. As an illustration, the first order case of fuzzy dominance rule for typical triangular fuzzy variables is examined.

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References

  1. Bawa, V.S.: Stochastic dominance: A research bibliography. Management Science 28, 698–712 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  2. Dachraoui, K., Dionne, G.: Stochastic dominance and optimal portfolio. Economics Letters 71, 347–354 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dana, R.A.: Market behavior when preferences are generated by second-order stochastic dominance. Journal of Mathematical Economics 40, 619–639 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. De Cooman, G.: Possibility theory-I, II, III. International Journal of General Systems 25, 291–371 (1997)

    Article  MATH  Google Scholar 

  5. Dentcheva, D., Ruszczynski, A.: Optimization with Stochastic Dominance Constraints. SIAM Journal on Optimization 14, 548–566 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dubois, D., Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York (1988)

    MATH  Google Scholar 

  7. Facchinetti, G., Ricci, R.G., Muzzioli, S.: Note on ranking fuzzy triangular numbers. International Journal of Intelligent Systems 13, 613–622 (1998)

    Article  Google Scholar 

  8. Iskander, M.G.: A suggested approach for possibility and necessity dominance indices in stochastic fuzzy linear programming. Applied Mathematics Letters 18, 395–399 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Levy, H.: Sochastic Dominance and Expected Utility: Survey and Analysis. Management Science 38, 555–593 (1992)

    Article  MATH  Google Scholar 

  10. Liu, B.: Uncertain Programming. John Wiley & Sons, New York (1999)

    Google Scholar 

  11. Liu, B.: Theory and Practice of Uncertain Programming. Physica, Heidelberg (2002)

    MATH  Google Scholar 

  12. Liu, B.: Uncertainty Theory: An Introduction to its Axiomatic Foundations. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  13. Liu, B., Iwamura, K.: Chance-constrained programming with fuzzy parameters. Fuzzy Sets and Systems 94, 227–237 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  14. Liu, B.: Dependent-chance programming in fuzzy environments. Fuzzy Sets and Systems 109, 95–104 (2000)

    Article  Google Scholar 

  15. Liu, B., Liu, Y.-K.: Expected value of fuzzy variable and fuzzy expected value model. IEEE Transactions on Fuzzy Systems 10, 445–450 (2002)

    Article  Google Scholar 

  16. Kaufmann, A.: Introduction to the Theory of Fuzzy Subsets. Academic Press, New York (1975)

    MATH  Google Scholar 

  17. Mitchell, H.B., Schaefer, P.A.: On ordering fuzzy numbers. International Journal of Intelligent Systems 15, 981–993 (2000)

    Article  MATH  Google Scholar 

  18. Nahmias, S.: Fuzzy variables. Fuzzy Sets and Systems 1, 97–100 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  19. Ogryczak, W., Ruszczyński, A.: From stochastic dominance to mean-risk models: Semideviations as risk measures. European Journal of Operational Research 116, 33–50 (1999)

    Article  MATH  Google Scholar 

  20. Peng, J., Liu, B.: Some properties of optimistic and pessimistic values of fuzzy variables. Proceedings of the Tenth IEEE International Conference on Fuzzy Systems 2, 292–295 (2004)

    MathSciNet  Google Scholar 

  21. Yager, R.R., Filev, D.: On ranking fuzzy numbers using valuations. International Journal of Intelligent Systems 14, 1249–1268 (1999)

    Article  MATH  Google Scholar 

  22. Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  23. Zadeh, L.A.: Fuzzy set as a basis for a theory of possibility. Fuzzy Sets and Systems 1, 3–28 (1978)

    Article  MATH  MathSciNet  Google Scholar 

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© 2005 Springer-Verlag Berlin Heidelberg

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Peng, J., Mok, H.M.K., Tse, WM. (2005). Fuzzy Dominance Based on Credibility Distributions. In: Wang, L., Jin, Y. (eds) Fuzzy Systems and Knowledge Discovery. FSKD 2005. Lecture Notes in Computer Science(), vol 3613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11539506_37

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  • DOI: https://doi.org/10.1007/11539506_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28312-6

  • Online ISBN: 978-3-540-31830-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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