Advertisement

An approach for parameterized shadowed type-2 fuzzy membership functions applied in control applications

  • Patricia Melin
  • Emanuel Ontiveros-Robles
  • Claudia I. Gonzalez
  • Juan R. Castro
  • Oscar CastilloEmail author
Methodologies and Application

Abstract

At present time, general type-2 fuzzy logic provides better uncertainty modeling when compared to interval type-2 fuzzy logic, and this has been shown with the improvement in the performance of fuzzy logic controllers and fuzzy edge detectors. However, higher computational cost represents a limitation for many applications and implementation platforms, and it is because of this that the computational cost reduction is the main goal of this paper. The aim of this work is to model a GT2 FLS based on shadowed type-2 fuzzy sets (ST2 FS) and apply this approach to control problems. The ST2 FS consists of approximating the secondary membership function by shadowed sets and is because of this, that we present an analytic approach to obtain the shadowed set for triangular and Gaussian membership functions for any parameters. Based on this, we achieve a representation of the ST2 FS as a parameterized function, facilitating its implementation. The results are compared against the performance when a generalized type-2 fuzzy inference system is approximated using α-planes for control applications.

Keywords

General type-2 fuzzy sets Shadowed sets Interval type-2 fuzzy sets Shadowed type-2 fuzzy sets 

Notes

Compliance with ethical standards

Conflict of interest

All the authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Arqub OA (2017) Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm-Volterra integrodifferential equations. Neural Comput Appl 28(7):1591–1610CrossRefGoogle Scholar
  2. Arqub OA, AL-Smadi M, Momani S, Hayat T (2016) Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method. Soft Comput 20(8):3283–3302CrossRefzbMATHGoogle Scholar
  3. Arqub OA, Al-Smadi M, Momani S, Hayat T (2017) Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems. Soft Comput 21(23):7191–7206CrossRefzbMATHGoogle Scholar
  4. Castillo O, Amador-Angulo L, Castro JR, Garcia-Valdez M (2016) A comparative study of type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems in control problems. Inf Sci 354:257–274CrossRefGoogle Scholar
  5. Castro JR, Castillo O, Melin P (2007) An interval type-2 fuzzy logic toolbox for control applications. IEEE Int Fuzzy Syst Conf 2007:1–6Google Scholar
  6. Coupland S, John R (2008) New geometric inference techniques for type-2 fuzzy sets. Int J Approx Reason 49(1):198–211MathSciNetCrossRefzbMATHGoogle Scholar
  7. Davoudkhani IF, Akbari M (2016) Adaptive speed control of brushless DC (BLDC) motor based on interval type-2 fuzzy logic. In: 2016 24th Iranian conference on electrical engineering (ICEE), pp. 1119–1124Google Scholar
  8. Deng X, Yao Y (2013) Mean-value-based decision-theoretic shadowed sets. In: 2013 Joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), pp. 1382–1387Google Scholar
  9. Dubchak L, Verbovyy S, Berezska K, Datsko T (1997) Fuzzy knowledge base for diagnosing breast cancer pathological processes. Artif Intell Med 11(1):75–85CrossRefGoogle Scholar
  10. Giger ML, Karssemeijer N, Schnabel JA (2013) Breast image analysis for risk assessment, detection, diagnosis, and treatment of cancer. Annu Rev Biomed Eng 15(1):327–357CrossRefGoogle Scholar
  11. Giribabu D, Vardhan RH, Prasad RR (2016) Multi level inverter fed indirect vector control of induction motor using type 2 fuzzy logic controller. In: 2016 international conference on electrical, electronics, and optimization techniques (ICEEOT), pp. 2605–2610Google Scholar
  12. Gonzalez CI, Melin P, Castillo O, Juarez D, Castro JR (2017) Toward general type-2 fuzzy logic systems based on shadowed sets. Adv Fuzzy Log Technol 2017:131–142Google Scholar
  13. Hagras H (2007) Type-2 FLCs: a new generation of fuzzy controllers. IEEE Comput Intell Mag 2(1):30–43CrossRefGoogle Scholar
  14. Hannan MA, Ghani ZA, Mohamed A, Uddin MN (2015) Real-time testing of a fuzzy-logic-controller-based grid-connected photovoltaic inverter system. IEEE Trans Ind Appl 51(6):4775–4784CrossRefGoogle Scholar
  15. Hasanien HM, Matar M (2015) A fuzzy logic controller for autonomous operation of a voltage source converter-based distributed generation system. IEEE Trans. Smart Grid 6(1):158–165CrossRefGoogle Scholar
  16. Linda O, Manic M (2012) Shadowed type-2 fuzzy sets -type-2 fuzzy sets with shadowed secondary membership functions. IEEE Int Conf Fuzzy Syst 2012:1–8Google Scholar
  17. Luo S-T, Cheng B-W (2012) Diagnosing breast masses in digital mammography using feature selection and ensemble methods. J Med Syst 36(2):569–577CrossRefGoogle Scholar
  18. Masmoudi MS, Krichen N, Masmoudi M, Derbel N (2016) Fuzzy logic controllers design for omnidirectional mobile robot navigation. Appl Soft Comput 49:901–919CrossRefGoogle Scholar
  19. Mendel JM (2010) Comments on α-plane representation for type-2 fuzzy sets: theory and applications. IEEE Trans Fuzzy Syst 18(1):229–230CrossRefGoogle Scholar
  20. Mendel JM (2014) General type-2 fuzzy logic systems made simple: a tutorial. IEEE Trans Fuzzy Syst 22(5):1162–1182CrossRefGoogle Scholar
  21. Mendel JM (2017) Uncertain rule-based fuzzy systems. Springer International Publishing, ChamCrossRefzbMATHGoogle Scholar
  22. Mendel JM, John RIB (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2):117–127CrossRefGoogle Scholar
  23. Mendel JM, Liu F, Zhai D (2009) α-plane representation for type-2 fuzzy sets: theory and applications. IEEE Trans Fuzzy Syst 17(5):1189–1207CrossRefGoogle Scholar
  24. Mitra S, Pedrycz W, Barman B (2010) Shadowed c-means: integrating fuzzy and rough clustering. Pattern Recognit 43(4):1282–1291CrossRefzbMATHGoogle Scholar
  25. Ofoli AR, Rubaai A (2006) Real-time implementation of a fuzzy logic controller for switch-mode power-stage DC ndash; DC converters. IEEE Trans Ind Appl 42(6):1367–1374CrossRefGoogle Scholar
  26. Ontiveros-Robles E, Melin P, Castillo O (2017) New methodology to approximate type-reduction based on a continuous root-finding karnik mendel algorithm. Algorithms 10(3):77MathSciNetCrossRefzbMATHGoogle Scholar
  27. Ontiveros-Robles E, Melin P, Castillo O (2018) Comparative analysis of noise robustness of type 2 fuzzy logic controllers. Kybernetika, 175–201Google Scholar
  28. Pedrycz W (1998) Shadowed sets: representing and processing fuzzy sets. IEEE Trans Syst Man Cybern Part B Cybern 28(1):103–109CrossRefGoogle Scholar
  29. Pedrycz W (2009) From fuzzy sets to shadowed sets: interpretation and computing. Int J Intell Syst 24(1):48–61CrossRefzbMATHGoogle Scholar
  30. Pedrycz W, Song M (2012) Granular fuzzy models: a study in knowledge management in fuzzy modeling. Int J Approx Reason 53(7):1061–1079MathSciNetCrossRefGoogle Scholar
  31. Pedrycz W, Vukovich G (1999) Granular computing in the development of fuzzy controllers. Int J Intell Syst 14(4):419–447CrossRefzbMATHGoogle Scholar
  32. Tahayori H, Sadeghian A (2013) Shadowed fuzzy sets: a framework with more freedom degrees for handling uncertainties than interval type-2 fuzzy sets and lower computational complexity than general type-2 fuzzy sets. N Concepts Appl Soft Comput 97–117Google Scholar
  33. Wagner C, Hagras H (2010) Toward general type-2 fuzzy logic systems based on zSlices. IEEE Trans Fuzzy Syst 18(4):637–660CrossRefGoogle Scholar
  34. Wagner C, Hagras H (2011) Employing zSlices based general type-2 fuzzy sets to model multi level agreement. In: 2011 IEEE symposium on advances in type-2 fuzzy logic systems (T2FUZZ), pp. 50–57Google Scholar
  35. Wijayasekara D, Linda O, Manic M (2013) Shadowed type-2 fuzzy logic systems. In: 2013 IEEE symposium on advances in type-2 fuzzy logic systems (T2FUZZ), pp. 15–22Google Scholar
  36. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353CrossRefzbMATHGoogle Scholar
  37. Zidani F, Diallo D, Benbouzid MEH, Nait-Said R (2008) A fuzzy-based approach for the diagnosis of fault modes in a voltage-Fed PWM inverter induction motor drive. IEEE Trans Ind Electron 55(2):586–593CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Tijuana Institute of TechnologyTijuanaMexico

Personalised recommendations