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Probability-Based Approach Explains (and Even Improves) Heuristic Formulas of Defuzzification

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Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11471))

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Abstract

Fuzzy techniques have been successfully used in many applications. However, often, formulas for processing fuzzy information are heuristic: they lack a convincing justification, and thus, users are sometimes reluctant to use them. In this paper, we show that we can justify (and sometimes even improve) these methods if we use a probability-based approach.

This work was supported in part by the US National Science Foundation grant HRD-1242122 (Cyber-ShARE Center of Excellence).

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References

  1. Belohlavek, R., Dauben, J.W., Klir, G.J.: Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press, New York (2017)

    MATH  Google Scholar 

  2. Bellman, R.E., Zadeh, L.A.: Decision making in a fuzzy environment. Manage. Sci. 17(4), B141–B164 (1970)

    Article  MathSciNet  Google Scholar 

  3. Coletti, G., Scozzafava, R.: Conditional probability and fuzzy information. Comput. Stat. Data Anal. 51(1), 115–132 (2006)

    Article  MathSciNet  Google Scholar 

  4. Coletti, G., Scozzafava, R., Vantaggi, B.: Possibility measures in probabilistic inference. In: Dubois, D., Lubiano, M.A., Prade, H., Gil, M.Á., Grzegorzewski, P., Hryniewicz, O. (eds.) Soft Methods for Handling Variability and Imprecision. Advances in Soft Computing, vol. 48, pp. 51–58. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85027-4_7

    Chapter  Google Scholar 

  5. Coletti, G., Scozzafava, R., Vantaggi, B.: A bridge between probability and possibility in a comparative framework. In: Liu, W. (ed.) ECSQARU 2011. LNCS (LNAI), vol. 6717, pp. 557–568. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22152-1_47

    Chapter  MATH  Google Scholar 

  6. Feynman, R., Leighton, R., Sands, M.: The Feynman Lectures on Physics. Addison Wesley, Boston (2005)

    MATH  Google Scholar 

  7. Huynh, V.-N., Nakamori, Y., Lawry, J.: A probability-based approach to comparison of fuzzy numbers and applications to target-oriented decision making. IEEE Trans. Fuzzy Syst. 16(2), 371–387 (2008)

    Article  Google Scholar 

  8. Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Prentice Hall, Upper Saddle River (1995)

    MATH  Google Scholar 

  9. Kosheleva, O., Kreinovich, V.: Why Bellman-Zadeh approach to fuzzy optimization. Appl. Math. Sci. 12(11), 517–522 (2018)

    Google Scholar 

  10. Lawry, J.: A voting mechanism for fuzzy logic. Int. J. Approximate Reasoning 19(3–4), 315–333 (1998)

    Article  MathSciNet  Google Scholar 

  11. Lawry, J.: Borderlines and probabilities of borderlines: on the interconnection between vagueness and uncertainty. J. Appl. Logic 14, 113–138 (2016)

    Article  MathSciNet  Google Scholar 

  12. Luce, R.D., Raiffa, H.: Games and Decisions: Introduction and Critical Survey. Dover, New York (1989)

    MATH  Google Scholar 

  13. Mendel, J.M.: Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-51370-6

    Book  MATH  Google Scholar 

  14. Myerson, R.B.: Game Theory: Analysis of Conflict. Harvard University Press, Harvard (1997)

    MATH  Google Scholar 

  15. Nguyen, H.T., Walker, E.A.: A First Course in Fuzzy Logic. Chapman and Hall/CRC, Boca Raton (2006)

    Google Scholar 

  16. Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer, Boston (1999)

    Book  Google Scholar 

  17. Thorne, K.S., Blandford, R.D.: Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics. Princeton University Press, Princeton (2017)

    MATH  Google Scholar 

  18. von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)

    MATH  Google Scholar 

  19. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

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Acknowledgments

The authors are greatly thankful to the anonymous referees for valuable suggestions.

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Authors and Affiliations

  1. Computer Science and Information Technology Systems Department, El Paso Community College, 919 Hunter, El Paso, TX, 79915, USA

    Christian Servin

  2. University of Texas at El Paso, El Paso, TX, 79968, USA

    Olga Kosheleva & Vladik Kreinovich

Authors
  1. Christian Servin
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  2. Olga Kosheleva
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  3. Vladik Kreinovich
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Corresponding author

Correspondence to Vladik Kreinovich .

Editor information

Editors and Affiliations

  1. Osaka University, Toyonaka, Osaka, Japan

    Hirosato Seki

  2. Institute for Chemical Research, Kyoto University, Uji, Kyoto, Japan

    Canh Hao Nguyen

  3. Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan

    Van-Nam Huynh

  4. Osaka University, Toyonaka, Osaka, Japan

    Masahiro Inuiguchi

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Servin, C., Kosheleva, O., Kreinovich, V. (2019). Probability-Based Approach Explains (and Even Improves) Heuristic Formulas of Defuzzification. In: Seki, H., Nguyen, C., Huynh, VN., Inuiguchi, M. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2019. Lecture Notes in Computer Science(), vol 11471. Springer, Cham. https://doi.org/10.1007/978-3-030-14815-7_9

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  • DOI: https://doi.org/10.1007/978-3-030-14815-7_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-14814-0

  • Online ISBN: 978-3-030-14815-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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