Memristor Crossbar-Based Hardware Implementation of Type-2 Fuzzy Membership Function and On-Chip Learning

Document Type : Original Article

Authors

1 Department of Electeical and Computer Engineering, University of Zanjan, Zanjan, Iran

2 Computer Department, Kermanshah University of Technology, Kermanshah, Iran

3 Department of Electrical Engineering, University of Zanjan, Zanjan, Iran

4 Department of Electrical Engineering, University of Guilan, Rasht, Iran

Abstract

Utilizing fuzzy techniques, especially fuzzy type-2, is one of the most widely used methods in machine learning to model uncertainty. In addition to algorithm provision, the hardware implementation capability, and proper performance in real-time applications are other challenges. The use of hardware platforms that have biological similarities and are comparable to human neural systems in terms of implementation volume has always been considered. Memristor is one of the emerging elements for the implementation of fuzzy logic based algorithms. In this element, by providing current and selecting the appropriate direction for the applied current, the resistance of the memristor (memristance) will increase or decrease. Various implementations of type-1 fuzzy systems exist, but no implementation of type-2 fuzzy systems has been done based on memristors. In this paper, memristor-crossbar structures are used to implement type-2 fuzzy membership functions. In the proposed hardware, the membership functions can have any shape and resolution. Our proposed implementation of type-2 fuzzy membership function has the potential to learn (On-Chip learning capability regardless of host system). Besides, the proposed hardware is analog and can be used as a basis in the construction of evolutionary systems. Furthermore, the proposed approach is applied to memristor emulator to demonstrate its correct operation.

Keywords


  1. Tanaka, K. and Wang, H.O., "Fuzzy control systems design and analysis: A linear matrix inequality approach, John Wiley & Sons, (2004).
  2. Terano, T., Asai, K. and Sugeno, M., "Applied fuzzy systems, Academic Press, (2014).
  3. Zadeh, L.A., Fu, K.-S. and Tanaka, K., "Fuzzy sets and their applications to cognitive and decision processes: Proceedings of the us–japan seminar on fuzzy sets and their applications, held at the university of california, berkeley, california, july 1-4, 1974, Academic press, (2014).
  4. Srikrishna, A., Reddy, B.E. and Srinivas, V.S., Detection of lesion in mammogram images using differential evolution based automatic fuzzy clustering, in Computational intelligence techniques in health care. 2016, Springer.61-68. doi.org/10.1007/978-981-10-0308-0_5
  5. Klidbary, S.H., Shouraki, S.B., Ghaffari, A. and Kourabbaslou, S.S., "Outlier robust fuzzy active learning method (alm)", in 2017 7th international conference on computer and knowledge engineering (ICCKE), IEEE. (2017), 347-352. doi: 10.1109/ICCKE.2017.8167903
  6. Mendel, J.M., Uncertain rule-based fuzzy systems, in Introduction and new directions. 2017, Springer.684. doi.org/10.1007/978-3-319-51370-6
  7. Mendel, J.M. and John, R.B., "Type-2 fuzzy sets made simple", IEEE Transactions on Fuzzy Systems, Vol. 10, No. 2, (2002), 117-127, doi: 10.1109/91.995115.
  8. John, R.I., Innocent, P.R. and Barnes, M., "Neuro-fuzzy clustering of radiographic tibia image data using type 2 fuzzy sets", Information Sciences, Vol. 125, No. 1-4, (2000), 65-82, doi.org/10.1016/S0020-0255(00)00009-8.
  9. Ozen, T. and Garibaldi, J.M., "Investigating adaptation in type-2 fuzzy logic systems applied to umbilical acid-base assessment", in Proceedings of 2003 European Symposium on Intelligent Technologies (EUNITE 2003). (2003), 289-294.
  10. Figueroa, J., Posada, J., Soriano, J., Melgarejo, M. and Rojas, S., "A type-2 fuzzy controller for tracking mobile objects in the context of robotic soccer games", in The 14th IEEE International Conference on Fuzzy Systems, 2005. FUZZ'05., IEEE. (2005), 359-364. doi: 10.1109/FUZZY.2005.1452420
  11. Melin, P., Mendoza, O. and Castillo, O., "An improved method for edge detection based on interval type-2 fuzzy logic", Expert Systems with Applications, Vol. 37, No. 12, (2010), 8527-8535, doi.org/10.1016/j.eswa.2010.05.023.
  12. Kim, D., " An implementation of fuzzy logic controller on the reconfigurable fpga system", IEEE Transactions on industrial Electronics, Vol. 47, No. 3, (2000), 703-715, doi: 10.1109/41.847911.
  13. Klidbary, S.H., Shouraki, S.B. and Linares-Barranco, B., "Digital hardware realization of a novel adaptive ink drop spread operator and its application in modeling and classification and on-chip training", International Journal of Machine Learning and Cybernetics, Vol. 10, No. 9, (2019), 2541-2561, doi: doi.org/10.1007/s13042-018-0890-x.
  14. Hung, D.L., "Dedicated digital fuzzy hardware", IEEE Micro, Vol. 15, No. 4, (1995), 31-39, doi: 10.1109/40.400640.
  15. Chua, L.O. and Kang, S.M., "Memristive devices and systems", Proceedings of the IEEE, Vol. 64, No. 2, (1976), 209-223, doi: 10.1109/PROC.1976.10092..
  16. Chua, L., "Memristor-the missing circuit element", IEEE Transactions on Circuit Theory, Vol. 18, No. 5, (1971), 507-519, doi: 10.1109/TCT.1971.1083337.
  17. Strukov, D.B., Snider, G.S., Stewart, D.R. and Williams, R.S., "The missing memristor found", Nature, Vol. 453, No. 7191, (2008), 80-83, doi: doi.org/10.1038/nature06932.
  18. Waser, R. and Aono, M., Nanoionics-based resistive switching memories, in Nanoscience and technology: A collection of reviews from nature journals. 2010, World Scientific.158-165.
  19. Kuekes, P., "Material implication: Digital logic with memristors", in Memristor and memristive systems symposium. Vol. 21, (2008).
  20. Tarkhan, M., Maymandi-Nejad, M., Haghzad Klidbary, S. and Bagheri Shouraki, S., "A bridge technique for memristor state programming", International Journal of Electronics, Vol. 107, No. 6, (2020), 1015-1030, doi.org/10.1080/00207217.2019.1692371.
  21. Mouttet, B., " Proposal for memristors in signal processing", in International Conference on Nano-Networks, Springer. Vol., No., (2008), 11-13. doi: 10.1007/978-3-642-02427-6_3
  22. Merrikh-Bayat, F. and Shouraki, S.B., "Memristor-based circuits for performing basic arithmetic operations", Procedia Computer Science, Vol. 3, (2011), 128-132, doi.org/10.1016/j.procs.2010.12.022.
  23. Amer, S., Madian, A.H. and Emara, A.S., " Memristor-based center-of-gravity (COG) defuzzifier circuit", in 2015 European Conference on Circuit Theory and Design (ECCTD), IEEE. (2015), 1-4. doi: 10.1109/ECCTD.2015.7300099
  24. Amer, S., Madian, A., ElSayed, H. and Emara, A., "Effect of the memristor threshold current on memristor-based min-max circuits", in 2016 5th International Conference on Modern Circuits and Systems Technologies (MOCAST), IEEE. (2016), 1-4. doi: 10.1109/MOCAST.2016.7495104
  25. Merrikh-Bayat, F., Shouraki, S.B. and Merrikh-Bayat, F., "Memristor crossbar-based hardware implementation of fuzzy membership functions", in 2011 eighth international conference on fuzzy systems and knowledge discovery (FSKD), IEEE. Vol. 1, (2011), 645-649.
  26. Merrikh-Bayat, F. and Shouraki, S.B., "Memristive neuro-fuzzy system", IEEE Transactions on Cybernetics, Vol. 43, No. 1, (2012), 269-285, doi.
  27. Merrikh-Bayat, F., Shouraki, S.B. and Rohani, A., "Memristor crossbar-based hardware implementation of the ids method", IEEE Transactions on Fuzzy Systems, Vol. 19, No. 6, (2011), 1083-1096, doi: 10.1109/TFUZZ.2011.2160024.
  28. Klidbary, S.H. and Shouraki, S.B., "A novel adaptive learning algorithm for low-dimensional feature space using memristor-crossbar implementation and on-chip training", Applied Intelligence, Vol. 48, No. 11, (2018), 4174-4191, doi.org/10.1007/s10489-018-1202-6.
  29. Klidbary, S.H., Shouraki, S.B. and Afrakoti, I.E.P., "An adaptive efficient memristive ink drop spread (IDS) computing system", Neural Computing and Applications, Vol. 31, No. 11, (2019), 7733-7754, doi.org/10.1007/s00521-018-3604-0.
  30. Afrakoti, I.E.P., Shouraki, S.B., Bayat, F.M. and Gholami, M., "Using a memristor crossbar structure to implement a novel adaptive real-time fuzzy modeling algorithm", Fuzzy Sets and Systems, Vol. 307, (2017), 115-128, doi.org/10.1016/j.fss.2016.02.016.
  31. Adhikari, S.P., Yang, C., Kim, H. and Chua, L.O., "Memristor bridge synapse-based neural network and its learning", IEEE Transactions on Neural Networks and Learning Systems, Vol. 23, No. 9, (2012), 1426-1435, doi: 10.1109/TNNLS.2012.2204770.
  32. Hasan, R., Taha, T.M. and Yakopcic, C., "On-chip training of memristor crossbar based multi-layer neural networks", Microelectronics Journal, Vol. 66, (2017), 31-40, doi.org/10.1016/j.mejo.2017.05.005.
  33. Li, T., Duan, S., Liu, J., Wang, L. and Huang, T., "A spintronic memristor-based neural network with radial basis function for robotic manipulator control implementation", IEEE Transactions on Systems, Man, and Cybernetics: Systems, Vol. 46, No. 4, (2015), 582-588, doi: 10.1109/TSMC.2015.2453138.
  34. Alibart, F., Zamanidoost, E. and Strukov, D.B., "Pattern classification by memristive crossbar circuits using ex situ and in situ training", Nature Communications, Vol. 4, No. 1, (2013), 1-7, doi: 10.1038/ncomms3072.
  35. Karnik, N.N. and Mendel, J.M., "Introduction to type-2 fuzzy logic systems", in 1998 IEEE international conference on fuzzy systems proceedings. IEEE world congress on computational intelligence (Cat. No. 98CH36228), IEEE. Vol. 2, (1998), 915-920.
  36. Karnik, N.N., Mendel, J.M. and Liang, Q., "Type-2 fuzzy logic systems", IEEE Transactions on Fuzzy Systems, Vol. 7, No. 6, (1999), 643-658, doi: 10.1109/FUZZY.1998.686240.
  37. Biolek, D., Di Ventra, M. and Pershin, Y.V., "Reliable spice simulations of memristors, memcapacitors and meminductors", arXiv preprint arXiv:1307.2717, (2013).