Soft Computing

, Volume 22, Issue 2, pp 571–594 | Cite as

A new fuzzy bee colony optimization with dynamic adaptation of parameters using interval type-2 fuzzy logic for tuning fuzzy controllers

Methodologies and Application

Abstract

This paper presents a new fuzzy bee colony optimization method to find the optimal distribution of the membership functions in the design of fuzzy controllers for complex nonlinear plants. We used interval type-2 and type-1 fuzzy logic systems in dynamically adapting the alpha and beta parameter values of the bee colony optimization algorithm (BCO). Simulation results with a type-1 fuzzy logic controller for benchmark control plants are presented. The advantage of using interval type-2 fuzzy logic systems for dynamic adjustment of parameters in BCO applied in fuzzy controller design is verified with two benchmark problems. We considered different levels and types of noise in the simulations to analyze the approach of interval type-2 fuzzy logic systems to find the best values of alpha and beta for BCO when applied in the design of fuzzy controllers.

Keywords

Interval type-2 fuzzy logic system Fuzzy controller Bio-inspired algorithm Footprint uncertainty Bee colony optimization 

Notes

Acknowledgments

This research work did not receive funding.

Compliance with ethical standards

Conflict of interest

All the authors in the paper 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. Amador-Angulo L, Castillo O (2013a) Comparison of fuzzy controllers for the water tank with type-1 and type-2 fuzzy logic. In: NAFIPS 2013, Edmonton, Canada, pp 1–6Google Scholar
  2. Amador-Angulo L, Castillo O (2013b) Comparison of the optimal design of fuzzy controllers for the water tank using ant colony optimization. In: Recent advances on hybrid approaches for designing intelligent systems, vol 547, Tijuana, B.C., pp 255–273Google Scholar
  3. Amador-Angulo L, Castillo O (2015) A new algorithm based in the smart behavior of the bees for the design of Mamdani-style fuzzy controllers using complex non-linear plants. In: Design of intelligent systems based on fuzzy logic, neural network and nature-inspired, optimization, pp 617–637Google Scholar
  4. Arabshahi P, Choi JJ, Marks RJ II, Caudell TP (1996) Fuzzy parameter adaptation in optimization: some neural net training examples. Comput Sci Eng 1:57–65CrossRefGoogle Scholar
  5. Astudillo L, Castillo O, Aguilar L (2007) Intelligent control for a perturbed autonomous wheeled mobile robot: a type-2 fuzzy logic approach. Nonlinear Stud 14(1):37–48Google Scholar
  6. Aung N, Cooper E, Hoshino Y, Kamei K (2007) A proposal of fuzzy control systems for trailers driven by multiple motors in side slipways to haul out ships. Int J Innov Comput Inf Control 3(4):799–812Google Scholar
  7. Bel A, Wagner C, Hagras H (2013) Multiobjective optimization and comparison of nonsingleton type-1 and singleton interval type-2 fuzzy logic systems. IEEE Trans Fuzzy Syst 21(3):459–476CrossRefGoogle Scholar
  8. Biesmeijer JC, Seeley TD (2005) The use of waggle dance information by honey bees throughout their foraging careers. Behav Ecol Sociobiol 59(1):133–142CrossRefGoogle Scholar
  9. Bonabeau E, Dorigo M, Theraulaz G (1997) Swarm intelligence. Oxford University Press, OxfordMATHGoogle Scholar
  10. Castillo O (2012) Interval type-2 Mamdani fuzzy systems for intelligent control, combining experimentation and theory. Springer, BerlinGoogle Scholar
  11. Castillo O, Melin P (2008) Type-2 fuzzy logic theory and applications. Springer, BerlinMATHGoogle Scholar
  12. Castillo O, Melin P (2012) A review on the design and optimization of interval type-2 fuzzy controllers. Appl Soft Comput (ASC) 12:1267–1278CrossRefGoogle Scholar
  13. Castillo O, Martinez R, Melin P (2010) Bio-inspired optimization of fuzzy logic controllers for robotic autonomous system with PSO and ACO. In: Fuzzy information engineering, pp 119–143Google Scholar
  14. Castillo O, Martinez-Marroquin R, Melin P, Valdez F, Soria J (2012) Comparative study of bio-inspired algorithms applied to the optimization of type-1 and type-2 fuzzy controllers for an autonomous mobile robot. Inf Sci 192:19–38CrossRefGoogle Scholar
  15. Castro JR, Castillo O, Melin P (2007) “An interval type-2 fuzzy logic toolbox for control applications. In: Fuzzy system conference, pp 1–6Google Scholar
  16. Cázarez-Castro N, Aguilar LT, Castillo O (2012) Designing type-1 and type-2 fuzzy logic controllers via fuzzy Lyapunov synthesis for nonsmooth mechanical systems. Eng Appl Artif Intell 25:971–979CrossRefGoogle Scholar
  17. Cervantes L, Castillo O, Melin P (2011) Intelligent control of nonlinear dynamic plants using a hierarchical modular approach and type-2 fuzzy logic. In: MICAI, pp 1–12Google Scholar
  18. Chaiyatham T, Ngamroo I (2012) A bee colony optimization based-fuzzy logic-PID control design of electrolyzer for microgrid stabilization. Int J Innov Comput Inf Control 8(9):6049–6066Google Scholar
  19. Chang WJ, Hsu FL (2015) Mamdani and Takagi-Sugeno fuzzy controller design for ship fin stabilizing systems. In: Fuzzy systems and knowledge discovery (FSKD), 2015 12th international conference on, pp 345–350. IEEEGoogle Scholar
  20. Chatterjee A, Siarry P (2006) Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization. Comput Oper Res 33(3):859–871CrossRefMATHGoogle Scholar
  21. Chen S, Chang Y, Pan J (2013) Fuzzy rules interpolation for sparse fuzzy rule-based systems based on interval type-2 gaussian fuzzy sets and genetic algorithms. IEEE Trans Fuzzy Syst 21(3):412–425CrossRefGoogle Scholar
  22. Chong Ch, Low M, Sivakumar AK, Gay (2006) A bee colony optimization algorithm to job shop scheduling. In: Proceedings of the 2006 winter simulation conference, pp 1959Google Scholar
  23. Dyler FC (2002) The biology of the dance language. Annu Rev Entomol 47:917–949CrossRefGoogle Scholar
  24. Hagras HA (2007) Type-2 FLC: a new generalization of fuzzy controllers. In: IEEE computational intelligence magazine, February, pp 30–43Google Scholar
  25. Hsu C, Juang C (2013) Evolutionary robot wall-following control using type-2 fuzzy controller with species-de-activated continuous aco. IEEE Trans Fuzzy Syst 21(1):100–112CrossRefGoogle Scholar
  26. Juang CF, Lu CM, Lo C, Wang CY (2008) Ant colony optimization algorithm for fuzzy controller design and its fpga implementation. Ind Electron IEEE Trans 55(3):1453–1462CrossRefGoogle Scholar
  27. Karnik NN, Mendel JM (2001) Operations on type-2 fuzzy sets. Int J Fuzzy Sets Syst 122:327–348MathSciNetCrossRefMATHGoogle Scholar
  28. Karnik NN, Mendel JM, Liang Q (1999) Type-2 fuzzy logic system. IEEE Trans Fuzzy Syst 7(6):643–658CrossRefGoogle Scholar
  29. Kayacan E, Ramon H, Kaynakand O, Saey W (2015) Towards agrobots: trajectory control of an autonomous tractor using type-2 fuzzy logic controllers. Mechatron IEEE/ASME Trans 20(1):287–298CrossRefGoogle Scholar
  30. Klir GJ, Yuan B (1995) Fuzzy sets and fuzzy logic: theory and applications. Practice Hall, New JereyMATHGoogle Scholar
  31. Liang Q, Mendel JM (2000) Interval type-2 fuzzy logic systems: theory and design. Fuzzy Syst IEEE Trans 8(5):535–550CrossRefGoogle Scholar
  32. Lučić P, Teodorović D (2003b) Vehicle routing problem with uncertain demand at nodes: the bee system and fuzzy logic approach. In: Verdegay JL (ed) Fuzzy sets in optimization. Springer, Berlin, pp 67–82Google Scholar
  33. Mamdani EH (1974) Applications of fuzzy algorithms for simple dynamic plant. Proc IEEE 121(12):1585–1588Google Scholar
  34. Martinez R, Castillo O, Aguilar L (2009) Optimization of type-2 fuzzy logic controllers for a perturbed autonomous wheeled mobile robot using genetic algorithms. Inf Sci 179(13):2158–2174CrossRefMATHGoogle Scholar
  35. Melendez A, Castillo O (2012) Optimization of type-2 fuzzy reactive controllers for an autonomous mobile robot. NaBIC 2012:207–211Google Scholar
  36. Melin P, Olivas F, Castillo O, Valdez F, Soria J, Valdez M (2013) Optimal design of fuzzy classification systems using PSO with dynamic parameter adaptation through fuzzy logic. Expert Syst Appl 40(8):1–12Google Scholar
  37. Mendel JM (2001) Uncertain rule-based fuzzy logic system: introduction and new directions. Practice Hall, New JerseyMATHGoogle Scholar
  38. Mendel JM (2010) A quantitative comparison of interval type-2 and type1 fuzzy logic systems: first results. In: Proceedings of the IEEE international conference on fuzzy systems (FUZZ), pp 1–8Google Scholar
  39. Mendel JM (2013) On KM algorithms for solving type-2 fuzzy set problems. IEEE Trans Fuzzy Syst 21(3):426–446CrossRefGoogle Scholar
  40. Mendel JM, John RIB (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2):117–127CrossRefGoogle Scholar
  41. Mendel JM, Hagras H, Tan W-W, Melek WW, Ying H (2014) Introduction to type-2 fuzzy logic control. Wiley, HobokenCrossRefMATHGoogle Scholar
  42. Mendel JM, Rajati MR, Sussner P (2016) On clarifying some definitions and notations used for type-2 fuzzy sets as well as some recommended changes. Inf Sci 340:337–345MathSciNetCrossRefGoogle Scholar
  43. Mizumoto M, Tanaka K (1976) Some properties of fuzzy sets of Type-2. In: Information and control, pp 312–340Google Scholar
  44. Ochoa P, Castillo O (2014) Differential evolution with dynamic adaptation of parameters of the optimization of fuzzy controller. In: Recent advance of hybrid approach for designing intelligent systems, pp 275–288Google Scholar
  45. Pagola M, Lopez-Molina C, Fernandez J, Barrenechea E, Bustince H (2013) Interval type-2 fuzzy sets constructed from several membership functions: application to the fuzzy thresholding algorithm. IEEE Trans Fuzzy Syst 21(2):230–244CrossRefGoogle Scholar
  46. Sepúlveda R, Rodriguez A, Castillo O, Sepúlveda R (2007) Experimental study of intelligent controllers under uncertainty using type-1 and type-2 fuzzy logic. Inf Sci 177(10):2023–22048CrossRefGoogle Scholar
  47. Shi Y, Eberhart RC (2001) Fuzzy adaptive particle swarm optimization. In: Evolutionary computation, 2001. Proceedings of the 2001 congress on, vol 1, pp 101–106. IEEEGoogle Scholar
  48. Siliciano B, Sciavicco L, Villani L, Oriolo G (2010) Robotics: modelling, planning and control, pp 415–418Google Scholar
  49. Teodorović D (2003) Transport modeling by multi-agent systems: a swarm intelligence approach. Transp Plan Technol 26(4):289–312CrossRefGoogle Scholar
  50. Teodorović D (2008) Swarm intelligence systems for transportation engineering: principles and applications. Transp Res Part C Emerg Technol 16(6):651–782CrossRefGoogle Scholar
  51. Tiacharoen S, Chatchanayuenyong T (2012) Design and development of an intelligent control by using bee colony optimization technique. Am J Appl Sci 9(9):1464–1471CrossRefGoogle Scholar
  52. Tong S, Zhang Q (2008) Robust stabilization of nonlinear time-delay interconnected systems via decentralized fuzzy control. Int J Innov Comput Inf Control 4(7):1567–1582Google Scholar
  53. Wang T, Tong S, Li Y (2009) Robust adaptive fuzzy control for nonlinear system with dynamic uncertainties based on backstepping. Int J Innov Comput Inf Control 5(9):2675–2688Google Scholar
  54. Wong LP, Chong ChS (2009) An efficient bee colony optimization algorithm for traveling salesman problem using frequency-based pruning. In: 7th international conference on industrial informatics (INDIN 2009), pp 775–782Google Scholar
  55. Wong LP, Hean Low MY, Chong ChS (2008) Bee colony optimization with local search for traveling salesman problem. In: Proceedings of Second Asia International Conference on Modelling and Simulation, pp 818–823Google Scholar
  56. Wu D (2013) Approaches for reducing the computational cost of interval type-2 fuzzy logic systems: overview and comparisons. IEEE Trans Fuzzy Syst 21(1):80–99CrossRefGoogle Scholar
  57. Ying H (2000) Fuzzy control and modeling: analytical foundations and applications. IEEE Press, PiscatawayCrossRefGoogle Scholar
  58. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353CrossRefMATHGoogle Scholar
  59. Zadeh LA (1975a) The concept of a lingüistic variable and its application to approximate reasoning. Part I. Inf Sci 8:199–249CrossRefMATHGoogle Scholar
  60. Zadeh LA (1975b) The concept of a lingüistic variable and its application to approximate reasoning. Part II. Inf Sci 8:301–357CrossRefMATHGoogle Scholar
  61. Zadeh LA (1997) Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, fuzzy sets and systems, vol 90. Elsevier, AmsterdamMATHGoogle Scholar
  62. Zhou H, Ying H (2013) A method for deriving the analytical structure of a broad class of typical interval type-2 Mamdani fuzzy controllers. IEEE Trans Fuzzy Syst 21(3):447–458CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Division of Graduate StudiesTijuana Institute of TechnologyTijuanaMexico

Personalised recommendations