| Title of paper:
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How to take into account monotonicity (and other properties) in centroid approach to fuzzy and intuitionistic fuzzy control
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| Author(s):
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Vladik Kreinovich  0000-0002-1244-1650
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| Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, Texas 79968, USA
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| vladik@utep.edu
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| Olga Kosheleva 0000-0003-2587-4209
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| Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, Texas 79968, USA
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| olgak@utep.edu
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 4, pages 486–495
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| DOI:
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https://doi.org/10.7546/nifs.2025.31.4.486-495
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| Download:
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 PDF (186 Kb, File info)
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| Abstract:
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In many application areas, there are skilled experts who excel in control and decision making. It is desirable to come up with an automated system that would use their skills to help others make similarly good decisions. Often, the experts can only formulate their skills in terms of rules that use imprecise ("fuzzy") words from natural language like "small". To transform these fuzzy rules into a precise control strategy, Zadeh designed special technique that he called fuzzy. This technique was later improved – e.g., by adding explicit information about what the experts consider not a good control; such addition is known as intuitionistic fuzzy technique. The problem that we consider in this paper in that in many cases, in addition to the fuzzy expert rules, we also have some extra knowledge about the function [math]\displaystyle{ \overline u(x) }[/math] – the function that describes what control to apply for a given input x. For example, it is often reasonable to require that this function is increasing: the larger x, the more control we should apply. In this paper, we use the general decision theory technique to show how this additional information can be incorporated into fuzzy and intuitionistic fuzzy control.
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| Keywords:
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Fuzzy sets, Intuitionistic fuzzy sets, Centroid defuzzification, Monotonicity, Decision theory.
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| AMS Classification:
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03B52, 03E72.
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| References:
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- Atanassov, K. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Verlag, Heidelberg.
- Barlow, R. E., Bartholomew, D. J., Bremner, J. M., & Brunk, H. D. (1972). Statistical Inference under Order Restrictions. The Theory and Application of Isotonic Regression. Wiley, New York.
- Belohlavek, R., Dauben, J. W., & Klir, G. J. (2017). Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press, New York.
- Feynman, R., Leighton, R., & Sands, M. (2005). The Feynman Lectures on Physics. Addison Wesley, Boston, Massachusetts.
- Fishburn, P. C. (1969). Utility Theory for Decision Making. John Wiley & Sons Inc., New York.
- Fishburn, P. C. (1988). Nonlinear Preference and Utility Theory. The John Hopkins Press, Baltimore, Maryland.
- Jaynes, E. T., & Bretthorst, G. L. (2003). Probability Theory: The Logic of Science. Cambridge University Press, Cambridge, UK.
- Klir, G., & Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic. Prentice Hall, Upper Saddle River, New Jersey.
- Kreinovich, V. (2014). Decision making under interval uncertainty (and beyond), In: Guo, P., & Pedrycz, W. (Eds.). Human-Centric Decision-Making Models for Social Sciences. Springer Verlag, pp. 163–193.
- Luce, R. D., & Raiffa, R. (1989). Games and Decisions: Introduction and Critical Survey. Dover, New York.
- Mendel, J. M. (2024). Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions. Springer, Cham, Switzerland.
- Nguyen, H, T., Kosheleva, O., & Kreinovich, V. (2009). Decision making beyond Arrow’s ‘impossibility theorem’, with the analysis of effects of collusion and mutual attraction. International Journal of Intelligent Systems, 24(1), 27–47.
- Nguyen, H. T., Kreinovich, V., Wu, B., & Xiang, G. (2012). Computing Statistics under Interval and Fuzzy Uncertainty. Springer Verlag, Berlin, Heidelberg.
- Nguyen, N. T., & Walker, E. A. (2019). A First Course in Fuzzy Logic. Chapman and Hall/CRC, Boca Raton, Florida.
- Novak, V., Perfilieva, I., & Mockor, J. (1999). Mathematical Principles of Fuzzy Logic. Kluwer, Boston, Dordrecht.
- Radhika, C., & Parvathi, R. (2016). Defuzzification of intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 22(5), 19–26.
- Raiffa, R. (1997). Decision Analysis. McGraw-Hill, Columbus, Ohio.
- Robertson, T., Wright, F. T., & Dykstra, R. L. (1988). Order Restricted Statistical Inference. Wiley, New York.
- Sheskin, D. J. (2011). Handbook of Parametric and Nonparametric Statistical Procedures. Chapman and Hall/CRC, Boca Raton, Florida.
- Thorne, K. S. & Blandford, R. D. (2021). Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics. Princeton University Press, Princeton, New Jersey.
- Van Broekhoven, E., & De Baets, B. (2005). A linguistic fuzzy model with a monotone rule base is not always monotone. Proceedings of the EUSFLAT-LFA’05, Barcelona, Spain, 2005, pp. 530–535.
- Vassilev, P. M., & Atanassov, K. T. (2019). Modifications and Extensions of Intuitionistic Fuzzy Sets. “Prof. Marin Drinov” Academic Publishing House, Sofia.
- Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.
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