Skip to main content

A Framework for Analysis of Granular Neural Networks

  • Conference paper
  • First Online:
  • 1076 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10313))

Abstract

Granular neural networks are neural networks which operate at the level of information granules. Granules, in turn, can be seen as collections of objects that exhibit similar structure or possess similar functionality. In this work we try to provide a comprehensive look at the problem of how granular, feed-forward neural networks conduct their computations, i.e. what is the interpretation for the connections and the neurons of such networks. The paper orbits around the assumption that the networks come from the superposition of their certain subnetworks which emulate membership functions for the granules. The superposition represents an aggregation of a certain number of granules into another one. This interpretation comes from a general granular tree-model that is constructed prior to the network and which describes a particular problem in a semantically understandable form.

This is a preview of subscription content, log in via an institution.

References

  1. Bargiela, A., Pedrycz, W.: Granular Computing: An Introduction. Kluwer Academic Publishers, Boston (2003). doi:10.1007/978-1-4615-1033-8

    Book  MATH  Google Scholar 

  2. Bazan, J.G.: Hierarchical classifiers for complex spatio-temporal concepts. In: Peters, J.F., Skowron, A., Rybiński, H. (eds.) Transactions on Rough Sets IX. LNCS, vol. 5390, pp. 474–750. Springer, Heidelberg (2008). doi:10.1007/978-3-540-89876-4_26

    Chapter  Google Scholar 

  3. Dong, Y., Xu, Y., Yu, S.: Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model. IEEE Trans. Fuzzy Syst. 17(6), 1366–1378 (2009). doi:10.1109/TFUZZ.2009.2032172

    Article  Google Scholar 

  4. Dubois, D., Prade, H.: Interval-valued fuzzy sets, possibility theory and imprecise probability. In: Proceedings of International Conference in Fuzzy Logic and Technology, pp. 314–319 (2005)

    Google Scholar 

  5. Ganivada, A., Dutta, S., Sankar, K.P.: Fuzzy rough granular neural networks, fuzzy granules, and classification. Theoret. Comput. Sci. 412, 5834–5843 (2011). doi:10.1016/j.tcs.2011.05.038

    Article  MathSciNet  MATH  Google Scholar 

  6. Ganivada, A., Ray, S.S., Sankar, K.P.: Fuzzy rough sets, and a granular neural network for unsupervised feature selection. Neural Netw. 48, 91–108 (2013). doi:10.1016/j.neunet.2013.07.008

    Article  MATH  Google Scholar 

  7. Herrera, F., Alonso, S., Chiclana, F., Herrera-Viedma, E.: Computing with words in decision making: foundations, trends and prospects. Fuzzy Optim. Decis. Making 8(4), 337–364 (2009). doi:10.1007/s10700-009-9065-2

    Article  MATH  Google Scholar 

  8. Hirota, K.: Concepts of probabilistic sets. Fuzzy Sets Syst. 5, 31–46 (1981). doi:10.1109/CDC.1977.271516

    Article  MathSciNet  MATH  Google Scholar 

  9. Nguyen, S.H., Bazan, J., Skowron, A., Nguyen, H.S.: Layered learning for concept synthesis. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B., Świniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 187–208. Springer, Heidelberg (2004). doi:10.1007/978-3-540-27794-1_9

    Chapter  Google Scholar 

  10. Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11(5), 341–356 (1982). doi:10.1007/BF01001956

    Article  MATH  Google Scholar 

  11. Pedrycz, W.: Shadowed sets: representing and processing fuzzy sets. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 28(1), 103–109 (1998). doi:10.1109/3477.658584

    Article  Google Scholar 

  12. Pedrycz, W.: Interpretation of clusters in the framework of shadowed sets. Pattern Recogn. Lett. 26, 2439–2449 (2005). doi:10.1016/j.patrec.2005.05.001

    Article  Google Scholar 

  13. Pedrycz, W.: Granular Computing: Analysis and Design of Intelligent Systems. CRC Press, Boca Raton (2013). doi:10.1201/b14862

    Book  Google Scholar 

  14. Pedrycz, W.: Hierarchical granular clustering: an emergence of information granules of higher type and higher order. IEEE Trans. Fuzzy Syst. 23(6), 2270–2283 (2015). doi:10.1109/TFUZZ.2015.2417896

    Article  Google Scholar 

  15. Pedrycz, W., Skowron, A., Kreinovich, V. (eds.): Handbook of Granular Computing. Wiley, New York (2008). doi:10.1002/9780470724163

    Book  Google Scholar 

  16. Pedrycz, W., Vukovich, G.: Granular neural networks. Neurocomputing 36, 205–224 (2001). doi:10.1016/S0925-2312(00)00342-8

    Article  MATH  Google Scholar 

  17. Song, M., Pedrycz, W.: From local neural networks to granular neural networks: a study in information granulation. Neurocomputing 74, 3931–3940 (2011). doi:10.1016/j.neucom.2011.08.009

    Article  Google Scholar 

  18. Szczuka, M., Skowron, A., Jankowski, A., Ślezak, D.: Granular systems: from granules to systems. In: Webster, J. (ed.) Wiley Encyclopedia of Electrical and Electronics Engineering. Wiley, Hoboken (2016). doi:10.1002/047134608X

    Chapter  Google Scholar 

  19. Zadeh, L.A.: Fuzzy sets. Philos. Psychol. 8, 333–353 (1965). doi:10.1016/S0019-9958(65)90241-X

    Article  Google Scholar 

  20. Zadeh, L.A.: Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst. 2(1), 111–127 (1997). doi:10.1016/S0165-0114(97)00077-8

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Julian Skirzyński .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Skirzyński, J. (2017). A Framework for Analysis of Granular Neural Networks. In: Polkowski, L., et al. Rough Sets. IJCRS 2017. Lecture Notes in Computer Science(), vol 10313. Springer, Cham. https://doi.org/10.1007/978-3-319-60837-2_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-60837-2_16

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60836-5

  • Online ISBN: 978-3-319-60837-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics