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Robustness of Higher-Order Fuzzy Sets

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Frontiers of Higher Order Fuzzy Sets

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Abstract

Robustness is an important metric in analysis and design of interval type-2 fuzzy logic systems (IT2 FLSs). This chapter presents a mathematical approach to determine the robustness of IT2 FLSs that have withTakag–Sugeno–Kang (TSK) structure. We present numerical examples to demonstrate how the developed methodologies can be applied. The presented approach herein provides a systematic method for robust analysis of IT2 FLSs to further enhance their applications.

The majority of this chapter has been adopted by the author’s previous work [1–5].

(Biglarbegian et al. 2011).

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References

  1. M.B. BiglarBegian, W.W. Melek, J.M. Mendel, Stability analysis of type-2 fuzzy systems. in Proceedings of IEEE World Congress on Computational Intelligence (WCCI), pp. 947–953, Hong Kong, June 2008

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  2. M. Biglarbegian, W.W. Melek, J.M. Mendel, On the stability of interval type-2 TSK fuzzy logic control systems. IEEE Trans actions on. Systems, Man and Cybernetics— PartB : Cybernetics 40(3), 798–818 (2010)

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  3. M. Biglarbegian, W.W. Melek, J.M. Mendel, On the robustness of type-1 and interval type-2 fuzzy logic systems in modeling. Elsevier:Inf o. Sci. 181(7), 1325–1347 (2011)

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  4. W.W. Melek, A. Goldenberg, The development of a robust fuzzy inference mechanism. Elsevier: Int. J. Approx. Reason. 39(1), 29–47 (2005)

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  5. M.J. Mendel, Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions Prentice-Hall, Upper Saddle River, NJ, 2001

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Author information

Authors and Affiliations

  1. School of Engineering University of Guelph, Guelph, Ontario, Canada

    Mohammad Biglarbegian

Authors
  1. Mohammad Biglarbegian
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Correspondence to Mohammad Biglarbegian .

Editor information

Editors and Affiliations

  1. Ryerson University, Toronto, Ontario, Canada

    Alireza Sadeghian

  2. Ryerson University, Toronto, Ontario, Canada

    Hooman Tahayori

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Biglarbegian, M. (2015). Robustness of Higher-Order Fuzzy Sets. In: Sadeghian, A., Tahayori, H. (eds) Frontiers of Higher Order Fuzzy Sets. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3442-9_2

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  • DOI: https://doi.org/10.1007/978-1-4614-3442-9_2

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-3441-2

  • Online ISBN: 978-1-4614-3442-9

  • eBook Packages: EngineeringEngineering (R0)

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