A review on the application of fuzzy transform in data and image compression


Fuzzy transform is a relatively recent fuzzy approximation method, mainly used for image and general data processing. Due to the growing interest in the application of fuzzy transform over the last years, it seems proper providing a review of the technique. In this paper, we recall F-transform-based compression methods for data and images. The related works are examined, their motivations are explained, and the theoretical foundations are described. To test practical abilities of the related works, benchmark with emphasis to quality and processing time is established and the corresponding graphs are commented.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11


  1. 1.


  2. 2.


  3. 3.



  1. Abdelaal M, Theel O (2013) An efficient and adaptive data compression technique for energy conservation in wireless sensor networks. In: 2013 IEEE conference on wireless sensor (ICWISE). IEEE, pp 124–129

  2. Abdelaal M, Theel O, Kuka C, Zhang P, Gao Y, Bashlovkina V, Nicklas D, Fränzle M (2016) Improving energy efficiency in qos-constrained wireless sensor networks. Int J Distrib Sensor Netw. https://doi.org/10.1155/2016/1576038

    Article  Google Scholar 

  3. Alikhani R, Zeinali M, Bahrami F, Shahmorad S, Perfilieva I (2017) Trigonometric \(f^m\)-transform and its approximative properties. Soft Comput 21(35673577 21):3567–3577

    Google Scholar 

  4. Antia HM (2002) Numerical methods for scientists and engineers, I. Birkhauser Verlag, Basel

    Google Scholar 

  5. Bashlovkina V, Abdelaal M, Theel O (2015) Fuzzycat: a novel procedure for refining the f-transform based sensor data compression. In: Proceedings of the 14th international conference on information processing in sensor networks. ACM, pp 340–341

  6. Bede B, Rudas IJ (2011) Approximation properties of fuzzy transforms. Fuzzy Sets Syst 180(1):20–40

    MathSciNet  Article  Google Scholar 

  7. Christopoulos C, Skodras A, Ebrahimi T (2000) The jpeg2000 still image coding system: an overview. IEEE Trans Consum Electron 46(4):1103–1127

    Article  Google Scholar 

  8. Deutsch P, Gailly J-L (1996) Zlib compressed data format specification version 3.3, Technical report

  9. Di Martino F, Sessa S (2007) Compression and decompression of images with discrete fuzzy transforms. Inf Sci 177(11):2349–2362

    MathSciNet  Article  Google Scholar 

  10. Di Martino F, Sessa S (2018) Multi-level fuzzy transforms image compression. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-018-0971-4

    Article  Google Scholar 

  11. Di Martino F, Loia V, Perfilieva I, Sessa S (2008) An image coding/decoding method based on direct and inverse fuzzy transforms. Int J Approx Reason 48(1):110–131

    Article  Google Scholar 

  12. Di Martino F, Loia V, Sessa S (2010) Fuzzy transforms for compression and decompression of color videos. Inf Sci 180(20):3914–3931

    MathSciNet  Article  Google Scholar 

  13. Di Martino F, Loia V, Perfilieva I, Sessa S (2013) Fuzzy transform for coding/decoding images: a short description of methods and techniques. Stud Fuzziness Soft Comput 298:139–146

    Article  Google Scholar 

  14. Di Martino F, Hurtik P, Perfilieva I, Sessa S (2014) A color image reduction based on fuzzy transforms. Inf Sci 266:101–111

    Article  Google Scholar 

  15. Di Martino F, Sessa S, Perfilieva I (2017) First order fuzzy transform for images compression. J Signal Inf Process 8(03):178

    Google Scholar 

  16. Gaeta M, Loia V, Tomasiello S (2015) Multisignal 1-d compression by f-transform for wireless sensor networks applications. Appl Soft Comput 30:329–340

    Article  Google Scholar 

  17. Gaeta M, Loia V, Tomasiello S (2016) Cubic b-spline fuzzy transforms for an efficient and secure compression in wireless sensor networks. Inf Sci 339:19–30

    MathSciNet  Article  Google Scholar 

  18. Gambhir D, Rajpal N (2015) Improved fuzzy transform based image compression and fuzzy median filter based its artifact reduction: pairfuzzy. Int J Mach Learn Cybern 6(6):935–952

    Article  Google Scholar 

  19. Gambhir D, Rajpal N (2017) Edge and fuzzy transform based image compression algorithm: Edgefuzzy, In: Artificial intelligence and computer vision. Springer, pp 115–142

  20. Ghofrani F, Helfroush MS (2011) A modified approach for image compression based on fuzzy transform. In: 2011 19th Iranian conference on electrical engineering (ICEE). IEEE, pp 1–6

  21. Gibbs NE, Poole WG, Stockmeyer PK (1976) An algorithm for reducing the bandwidth and profile of a sparse matrix. SIAM J Numer Anal 13(2):236–250

    MathSciNet  Article  Google Scholar 

  22. Horn RA, Johnson CR (1985) Matrix analysis. Cambridge University Press, Cambridge

    Google Scholar 

  23. Huffman DA (1952) A method for the construction of minimum-redundancy codes. Proc IRE 40(9):1098–1101

    Article  Google Scholar 

  24. Hurtik P, Perfilieva I (2013a) Image compression methodology based on fuzzy transform using block similarity. In: 8th conference of the European society for fuzzy logic and technology, EUSFLAT 2013—advances in intelligent systems research. pp 521–526

  25. Hurtik P, Perfilieva I (2013b) Image compression methodology based on fuzzy transform. In: International joint conference CISIS12-ICEUTE’ 12-SOCO’ 12 special sessions. Springer, pp 525–532

  26. Hurtik P, Perfilieva I (2017) A hybrid image compression algorithm based on jpeg and fuzzy transform. In: 2017 IEEE international conference on fuzzy systems (FUZZ-IEEE). IEEE, pp 1–6

  27. Hurtik P, Perfilieva I (2018) Noise influence in fzt+jpeg image compression: accepted. In: FLINS 2018. pp 1–7

  28. Hyndman RJ, Koehler AB (2006) Another look at measures of forecast accuracy. Int J Forecast 22(4):679–688

    Article  Google Scholar 

  29. Jahedi S, Javadi F, Mehdipour M (2018) Compression and decompression based on discrete weighted transform. Appl Math Comput 335:133–145

    MathSciNet  Google Scholar 

  30. Khastan A (2017) A new representation for inverse fuzzy transform and its application. Soft Comput 21(13):3503–3512

    Article  Google Scholar 

  31. Loia V, Tomasiello S, Vaccaro A (2017) Fuzzy transform based compression of electric signal waveforms for smart grids. IEEE Trans Syst Man Cybern Syst 47(1):121–132

    Article  Google Scholar 

  32. Luo JC (1992) Algorithms for reducing the bandwidth and profile of a sparse matrix. Comput Struct 44(3):535–548

    MathSciNet  Article  Google Scholar 

  33. Miano J (1999) Compressed image file formats: Jpeg, png, gif, xbm, bmp. Addison-Wesley Professional, Boston

    Google Scholar 

  34. Novák V, Perfilieva I, Holčapek M, Kreinovich V (2014) Filtering out high frequencies in time series using f-transform. Inf Sci 274:192–209

    MathSciNet  Article  Google Scholar 

  35. Patanè G (2011) Fuzzy transform and least-squares approximation: analogies, differences, and generalizations. Fuzzy Sets Syst 180(1):41–54

    MathSciNet  Article  Google Scholar 

  36. Paternain D, Jurio A, Ruiz-Aranguren J, Minárová M, Takáč Z, Bustince H (2017) Optimized fuzzy transform for image compression. In: Advances in fuzzy logic and technology 2017. Springer, pp 118–128

  37. Pennebaker WB, Mitchell JL (1992) JPEG: Still image data compression standard. Springer, Berlin

    Google Scholar 

  38. Perfilieva I (2004) Fuzzy transform: application to the reef growth problem. In: Demicco RV, Klir GJ (eds) Fuzzy logic in geology. Elsevier, pp 275–300

  39. Perfilieva I (2005) Fuzzy transforms and their applications to image compression, In: International Workshop on Fuzzy Logic and Applications, Springer, pp. 19–31

  40. Perfilieva I (2006a) Fuzzy transforms: theory and applications. Fuzzy Sets Syst 157:993–1023

    MathSciNet  Article  Google Scholar 

  41. Perfilieva I (2006b) Fuzzy transforms: theory and applications. Fuzzy Sets Syst 157(8):993–1023

    MathSciNet  Article  Google Scholar 

  42. Perfilieva I, De Beats B (2010) Fuzzy transforms of monotone functions with application to image compression. Inf Sci 180:3304–3315

    MathSciNet  Article  Google Scholar 

  43. Perfilieva I, Haldeeva E (2001) Fuzzy transformation. In: IFSA world congress and 20th NAFIPS international conference, 2001. Joint 9th, vol 4. IEEE, pp 1946–1948

  44. Perfilieva I, Valásek R (2005) Data compression on the basis of fuzzy transforms. In: EUSFLAT conference, Citeseer. pp 663–668

  45. Perfilieva I, Vlašánek P (2013) Influence of various types of basic functions on image reconstruction using f-transform. In: 8th conference of the european society for fuzzy logic and technology, EUSFLAT 2013—advances in intelligent systems research. pp 497–502

  46. Perfilieva I, Daňková M, Bede B (2011) Towards a higher degree f-transform. Fuzzy Sets Syst 180(1):3–19

    MathSciNet  Article  Google Scholar 

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

    MathSciNet  Article  Google Scholar 

  48. Perfilieva I, Holčapek M, Kreinovich V (2016b) A new reconstruction from the f-transform components. Fuzzy Sets Syst 288:3–25

    MathSciNet  Article  Google Scholar 

  49. Perfilieva I, Hurtik P, Di Martino F, Sessa S (2017) Image reduction method based on the f-transform. Soft Comput 21(7):1847–1861

    Article  Google Scholar 

  50. Perfilieva I, Pavliska V, Vajgl M, De Baets B et al (2008) Advanced image compression on the basis of fuzzy transforms. In: Proceedings of the conference on IPMU. pp 1167–1174

  51. Rao KR, Yip P (2014) Discrete cosine transform: algorithms, advantages, applications. Academic press, New York

    Google Scholar 

  52. Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) Gsa: a gravitational search algorithm. Inf Sci 179(13):2232–2248

    Article  Google Scholar 

  53. Sztyber A (2014) Analysis of usefulness of a fuzzy transform for industrial data compression. In: Journal of physics: conference series, vol 570. IOP Publishing, p 042002

  54. Vlašánek P (2013) Generating suitable basic functions used in image reconstruction by f-transform. Adv Fuzzy Syst 4:1–6

    MATH  Google Scholar 

  55. Wang Z, Bovik AC, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612

    Article  Google Scholar 

  56. Yamamoto T, Ikebe Y (1979) Inversion of band matrices. Linear Algebra Appl 24:105–111

    MathSciNet  Article  Google Scholar 

  57. Zeinali M, Alikhani R, Shahmorad S, Bahrami F, Perfilieva I (2018) On the structural properties of fm-transform with applications. Fuzzy Sets Syst 342:32–52

    Article  Google Scholar 

  58. Ziv J, Lempel A (1977) A universal algorithm for sequential data compression. IEEE Trans Inf Theory 23(3):337–343

    MathSciNet  Article  Google Scholar 

Download references


This research was supported by the project “LQ1602 IT4Innovations excellence in science”.

Author information



Corresponding author

Correspondence to Petr Hurtik.

Ethics declarations

Conflict of interest

Authors Petr Hurtik and Stefania Tomasiello declare that they have no conflict of interest.

Human participants or animals performed

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

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Communicated by V. Loia.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hurtik, P., Tomasiello, S. A review on the application of fuzzy transform in data and image compression. Soft Comput 23, 12641–12653 (2019). https://doi.org/10.1007/s00500-019-03816-8

Download citation


  • F-transform
  • Data compression
  • Image compression
  • Fuzzy partition