Abstract
In many practical situations, we need to optimize the objective function under fuzzy constraints. Formulas for such optimization are known since the 1970s paper by Richard Bellman and Lotfi Zadeh, but these formulas have a limitation: small changes in the corresponding degrees can lead to a drastic change in the resulting selection. In this paper, we propose a natural modification of this formula, a modification that no longer has this limitation. Interestingly, this formula turns out to be related to formulas to skewed (asymmetric) generalizations of the normal distribution.
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References
Azzalini, A., Capitanio, A.: The Skew-Normal and Related Families. Cambridge University Press, Cambridge (2013)
Bellman, R.E., Zadeh, L.A.: Decision making in a fuzzy environment. Manag. Sci. 17(4), B 141–B 164 (1970)
Belohlavek, R., Dauben, J.W., Klir, G.J.: Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press, New York (2017)
Flores Muñiz, J.G., Kalashnikov, V.V., Kalashnykova, N., Kosheleva, O., Kreinovich, V.: Why skew normal: a simple pedagogical explanation. Int. J. Intell. Technol. Appl. Stat. 11(2), 113–120 (2018)
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)
Kreinovich, V., Kosheleva, O., Shahbazova, S.: Which t-norm is most appropriate for Bellman-Zadeh optimization. In: Shahbazova, S.N., Kacprzyk, J., Balas, V.E., Kreinovich, V. (eds.) Proceedings of the World Conference on Soft Computing, Baku, Azerbaijan, 29–31 May 2018 (2018)
Li, B., Shi, D., Wang, T.: Some applications of one-sided skew distributions. Int. J. Intell. Technol. Appl. Stat. 2(1), 13–27 (2009)
Mendel, J.M.: Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions. Springer, Cham (2017)
Nguyen, H.T., Walker, C.L., Walker, E.A.: A First Course in Fuzzy Logic. Chapman and Hall/CRC, Boca Raton (2019)
Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer, Boston/Dordrecht (1999)
Sheskin, D.J.: Handbook of Parametric and Nonparametric Statistical Procedures. Chapman and Hall/CRC, Boca Raton (2011)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Acknowledgments
This work was supported in part by the National Science Foundation grants 1623190 (A Model of Change for Preparing a New Generation for Professional Practice in Computer Science) and HRD-1242122 (Cyber-ShARE Center of Excellence).
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Kosheleva, O., Kreinovich, V., Nguyen, H.P. (2021). Optimization Under Fuzzy Constraints: Need to Go Beyond Bellman-Zadeh Approach and How It Is Related to Skewed Distributions. In: Phuong, N.H., Kreinovich, V. (eds) Soft Computing: Biomedical and Related Applications. Studies in Computational Intelligence, vol 981. Springer, Cham. https://doi.org/10.1007/978-3-030-76620-7_15
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DOI: https://doi.org/10.1007/978-3-030-76620-7_15
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