Abstract
A new class of fuzzy inference system is introduced, a probabilistic fuzzy inference system, for the modeling and control problems, one that model and minimize the effects of uncertainties, i.e., existing randomness in many real-world systems. The fusion of two different concepts, degree of truth and probability of truth in a distinctive framework leads to this new concept. This combination is carried out both in fuzzy sets and fuzzy rules, which gives rise to probabilistic fuzzy sets and probabilistic fuzzy rules. Consuming these probabilistic elements, a distinctive probabilistic fuzzy inference system is developed as a fuzzy probabilistic model, which improves the stochastic modeling capability. This probabilistic fuzzy inference system involves fuzzification, inference and output processing. The output processing includes order reduction and defuzzification. This integrated approach accounts for all of the uncertainty like rule uncertainties and measurement uncertainties present in the systems and has led to the design which performs optimally after training. A probabilistic fuzzy inference system is applied for modeling and control of a continuous stirred tank reactor process, which exhibits dynamic nonlinearity and demonstrated its improved performance over the conventional fuzzy inference system.
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Zadeh L.A.: The concept of a linguistic variable and its application to approximate reasoning—I. Inf. Sci. 8, 199–249 (1975). doi:10.1016/0020-0255(75)90036-5
Zadeh L.A.: Discussion: probability theory and fuzzy logic are complementary rather than competitive. Technometrics 37, 271–276 (1995). doi:10.2307/1269908
Bart Kosko J.: Fuzziness vs. probability. Int. J. Gen. Syst. 17, 211–240 (1990). doi:10.1080/03081079008935108
Liang P., Song F.: What does a probabilistic interpretation of fuzzy sets mean?. IEEE Trans. Fuzzy Syst. 2, 200–205 (1996). doi:10.1109/91.493913
Laviolette M., Seaman J.W. Jr: Unity and diversity of fuzziness-from a probability viewpoint. IEEE Trans. Fuzzy Syst. 2, 38–42 (1994). doi:10.1109/91.273123
Colubi A., Fernandez-Garcia C., Gil M.A.: Simulation of random fuzzy variables: an empirical approach to statistical/probabilistic studies with fuzzy experimental data. IEEE Trans. Fuzzy Syst. 10, 384–390 (2003). doi:10.1109/TFUZZ.2002.1006441
Meghdadi, A.H.; Akbarzadeh-T, M.R.: Probabilistic fuzzy logic and probabilistic fuzzy system. In: IEEE International Fuzzy Systems Conference, pp. 1127–1130 (2001)
Gorzalczany M.B.: A method of inference in approximate reasoning based on interval-valued fuzzy Sets. Fuzzy Sets Syst. 21, 1–17 (1987). doi:10.1016/0165-0114(87)90148-5
Bustince H., Burillo P.: Mathematical analysis of interval-valued fuzzy relations: application to approximate reasoning. Fuzzy Sets Syst. 113, 205–219 (2000). doi:10.1016/S0165-0114(98)00020-7
Karnik, N.N.; Mendel, J.M.: Introduction to type-2 fuzzy logic systems. IEEE, pp. 915–920 (1998). doi:10.1109/FUZZY.1998.686240
Mendel J.M., John R.I.B.: Type-2 fuzzy sets made simple. IEEE Trans. Fuzzy Syst. 10, 117–127 (2002). doi:10.1109/91.995115
Karnik N.N., Mendel J.M., Liang Q.: Type-2 fuzzy logic systems. IEEE Trans. Fuzzy Syst. 7, 643–658 (1999). doi:10.1109/91.811231
Liu Z., Li H.-X.: A probabilistic fuzzy logic system for modeling and control. IEEE Trans. Fuzzy Syst. 13, 848–856 (2005). doi:10.1109/TFUZZ.2005.859326
Prakash J., Srinivasan K.: Design of nonlinear PID controller and nonlinear model predictive controller for a continuous stirred tank reactor. Elsevier ISA Trans. 48, 273–282 (2009). doi:10.1016/j.isatra.2009.02.001
Sugeno M., Yasukawa T.: A fuzzy-logic-based approach to qualitative modeling. IEEE Trans. Fuzzy Syst. 1, 7–31 (1993). doi:10.1109/TFUZZ.1993.390281
Yager R.R.: Fuzzy modeling for intelligent decision making under uncertainty. IEEE Trans. Syst. Man Cybern. Part B Cybern. 30, 60–70 (2000). doi:10.1109/3477.826947
Senthil R., Janarthanan K., Prakash J.: Nonlinear state estimation using fuzzy Kalman filter. Ind. Eng. Chem. Res. 45, 8678–8688 (2006). doi:10.1021/ie0601753
Takagi T., Sugeno M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 15, 116–132 (1985). doi:10.1109/TSMC.1985.6313399
Zafiriou M.: Robust Process Control. Prentice Hall, Englewood Cliffs (1989)
Guillaume S.: Designing fuzzy inference systems from data: an interpretability-oriented review. IEEE Trans. Fuzzy Syst. 9, 426–443 (2001). doi:10.1109/91.928739
Wang L.-X., Mendel J.M.: Generating fuzzy rules by learning from examples. IEEE Trans. Syst. Man Cybern. 22, 1414–1427 (1992). doi:10.1109/21.199466
Wu D.: On the fundamental differences between interval type-2 and type-1 fuzzy logic controllers. IEEE Trans. Fuzzy Syst. 20, 832–848 (2012). doi:10.1109/TFUZZ.2012.2186818
Micco M., Coseza B.: Control of a distillation column by type-2 and type-1 fuzzy logic PID controllers. J. Process Control 24, 475–484 (2014). doi:10.1016/j.jprocont.2013.12.007
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Sozhamadevi, N., Sathiyamoorthy, S. A Probabilistic Fuzzy Inference System for Modeling and Control of Nonlinear Process. Arab J Sci Eng 40, 1777–1791 (2015). https://doi.org/10.1007/s13369-015-1627-8
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DOI: https://doi.org/10.1007/s13369-015-1627-8