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A new representation for inverse fuzzy transform and its application

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Abstract

In this study, a new representation formula for basic functions of fuzzy transform is introduced and some new approximating properties of the inverse fuzzy transform are described. In particular, using block pulse functions, we present properties of sinusoidal basic functions. As an application, we present a new fuzzy-based method for numerical solution of nonlinear Fredholm integral equations.

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References

  • Atkinson KE (1992) A survey of numerical methods for solving nonlinear integral equations. J Integral Equ Appl 4:15–46

    Article  MathSciNet  MATH  Google Scholar 

  • Atkinson KE (1997) The numerical solution of integral equations of the second kind. Cambridge University Press, New York

    Book  MATH  Google Scholar 

  • Babolian E, Shahsavaran A (2009) Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets. J Comput Appl Math 225:87–95

    Article  MathSciNet  MATH  Google Scholar 

  • Bede B (2013) Mathematics of fuzzy sets and fuzzy logic. Springer, London

    Book  MATH  Google Scholar 

  • Bede B, Rudas IJ (2011) Approximation properties of fuzzy transforms. Fuzzy Sets Syst 180:20–40

    Article  MathSciNet  MATH  Google Scholar 

  • Deb A, Dasgupta A, Sarkar G (2006) A new set of orthogonal functions and its application to the analysis of dynamic systems. J Franklin Inst 343:1–26

    Article  MathSciNet  MATH  Google Scholar 

  • Khastan A, Perfilieva I, Alijani Z (2016) A new fuzzy approximation method to Cauchy problems by fuzzy transform. Fuzzy Sets Syst 288:75–95

    Article  MathSciNet  Google Scholar 

  • Khastan A, Alijani Z, Perfilieva I (2016b) Fuzzy transform to approximate solution of two-point boundary value problems. Math Methods Appl Sci. doi:10.1002/mma.3832

  • Perfilieva I (2003) Fuzzy logic in geology, Chap. 9. In: Demicco RV, Klir GJ (eds) Fuzzy transform: application to the reef growth problem. Academic Press, Amsterdam, pp 275–300

    Google Scholar 

  • Perfilieva I (2006) Fuzzy transform: theory and applications. Fuzzy Sets Syst 157:993–1023

    Article  MathSciNet  MATH  Google Scholar 

  • Perfilieva I, Hodáková P, Hurtík P (2016) Differentiation by the F-transform and application to edge detection. Fuzzy Sets Syst 288:96–114

    Article  MathSciNet  MATH  Google Scholar 

  • Perfilieva I, Novak V, Dvorak A (2008) Fuzzy transform in the analysis of data. Int J Approx Reason 48:36–46

    Article  MATH  Google Scholar 

Download references

Acknowledgements

The author is grateful to the Editor and the anonymous Reviewer for their interesting and valuable comments. The author thanks Prof. Irina Perfilieva for her helpful comments and suggestions that greatly improved the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan, 45137-66731, Iran

    A. Khastan

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  1. A. Khastan
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Correspondence to A. Khastan.

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This article does not contain any studies with animals performed by author.

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Communicated by F. Di Martino, V. Novákc.

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Khastan, A. A new representation for inverse fuzzy transform and its application. Soft Comput 21, 3503–3512 (2017). https://doi.org/10.1007/s00500-017-2555-1

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  • DOI: https://doi.org/10.1007/s00500-017-2555-1

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