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A Probabilistic Fuzzy Inference System for Modeling and Control of Nonlinear Process

  • Research Article - Systems Engineering
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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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References

  1. 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

    Article  MATH  MathSciNet  Google Scholar 

  2. Zadeh L.A.: Discussion: probability theory and fuzzy logic are complementary rather than competitive. Technometrics 37, 271–276 (1995). doi:10.2307/1269908

    Article  Google Scholar 

  3. Bart Kosko J.: Fuzziness vs. probability. Int. J. Gen. Syst. 17, 211–240 (1990). doi:10.1080/03081079008935108

    Article  MATH  Google Scholar 

  4. 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

    Article  Google Scholar 

  5. 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

    Article  Google Scholar 

  6. 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

    Article  Google Scholar 

  7. Meghdadi, A.H.; Akbarzadeh-T, M.R.: Probabilistic fuzzy logic and probabilistic fuzzy system. In: IEEE International Fuzzy Systems Conference, pp. 1127–1130 (2001)

  8. 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

    Article  MATH  MathSciNet  Google Scholar 

  9. 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

    Article  MATH  MathSciNet  Google Scholar 

  10. Karnik, N.N.; Mendel, J.M.: Introduction to type-2 fuzzy logic systems. IEEE, pp. 915–920 (1998). doi:10.1109/FUZZY.1998.686240

  11. 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

    Article  Google Scholar 

  12. 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

    Article  Google Scholar 

  13. 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

    Article  Google Scholar 

  14. 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

    Article  Google Scholar 

  15. 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

    Article  Google Scholar 

  16. 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

    Article  Google Scholar 

  17. 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

    Article  Google Scholar 

  18. 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

    Article  MATH  Google Scholar 

  19. Zafiriou M.: Robust Process Control. Prentice Hall, Englewood Cliffs (1989)

    Google Scholar 

  20. 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

    Article  Google Scholar 

  21. 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

    Article  MathSciNet  Google Scholar 

  22. 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

    Article  Google Scholar 

  23. 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

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Electronics and Communication Engineering, Anna University, BIT Campus, Tiruchirappalli, Tamilnadu, India

    N. Sozhamadevi

  2. Department of Electronics and Instrumentation Engineering, JJ College of Engineering and Technology, Tiruchirappalli, Tamilnadu, India

    S. Sathiyamoorthy

Authors
  1. N. Sozhamadevi
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  2. S. Sathiyamoorthy
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Correspondence to N. Sozhamadevi.

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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

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