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
Belohlavek, R., Dauben, J.W., Klir, G.J.: Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press, New York (2017)
Bellman, R.E., Zadeh, L.A.: Decision making in a fuzzy environment. Manage. Sci. 17(4), B141–B164 (1970)
Coletti, G., Scozzafava, R.: Conditional probability and fuzzy information. Comput. Stat. Data Anal. 51(1), 115–132 (2006)
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
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
Feynman, R., Leighton, R., Sands, M.: The Feynman Lectures on Physics. Addison Wesley, Boston (2005)
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)
Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Prentice Hall, Upper Saddle River (1995)
Kosheleva, O., Kreinovich, V.: Why Bellman-Zadeh approach to fuzzy optimization. Appl. Math. Sci. 12(11), 517–522 (2018)
Lawry, J.: A voting mechanism for fuzzy logic. Int. J. Approximate Reasoning 19(3–4), 315–333 (1998)
Lawry, J.: Borderlines and probabilities of borderlines: on the interconnection between vagueness and uncertainty. J. Appl. Logic 14, 113–138 (2016)
Luce, R.D., Raiffa, H.: Games and Decisions: Introduction and Critical Survey. Dover, New York (1989)
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
Myerson, R.B.: Game Theory: Analysis of Conflict. Harvard University Press, Harvard (1997)
Nguyen, H.T., Walker, E.A.: A First Course in Fuzzy Logic. Chapman and Hall/CRC, Boca Raton (2006)
Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer, Boston (1999)
Thorne, K.S., Blandford, R.D.: Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics. Princeton University Press, Princeton (2017)
von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
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The authors are greatly thankful to the anonymous referees for valuable suggestions.
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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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