Document Type: Research Paper




In this study, we introduce and study a concept of distributed fuzzy
modeling. Fuzzy modeling encountered so far is predominantly of a centralized
nature by being focused on the use of a single data set. In contrast to this style of
modeling, the proposed paradigm of distributed and collaborative modeling is
concerned with distributed models which are constructed in a highly collaborative
fashion. In a nutshell, distributed models reconcile and aggregate findings of the
individual fuzzy models produced on a basis of local data sets. The individual
models are formed in a highly synergistic, collaborative manner. Given the fact that
fuzzy models are inherently granular constructs that dwell upon collections of
information granules – fuzzy sets, this observation implies a certain general
development process. There are two fundamental design issues of this style of
modeling, namely (a) a formation of information granules carried out on a basis of
locally available data and their collaborative refinement, and (b) construction of
local models with the use of properly established collaborative linkages. We discuss
the underlying general concepts and then elaborate on their detailed development.
Information granulation is realized in terms of fuzzy clustering. Local models
emerge in the form of rule-based systems. The paper elaborates on a number of
mechanisms of collaboration offering two general categories of so-called
horizontal and vertical clustering. The study also addresses an issue of
collaboration in cases when such interaction involves information granules formed
at different levels of specificity (granularity). It is shown how various algorithms of
collaboration lead to the emergence of fuzzy models involving information
granules of higher type such as e.g., type-2 fuzzy sets.


[1] R. Agarwal and R. Srikant, Privacy-preserving data mining., Proc. of the ACM SIGMOD
Conference on Management of Data, ACM Press, New York, May (2000), 439–450.
[2] A. M. Bensaid, L. O. Hall, J. C. Bezdek and L. P. Clarke. Partially supervised clustering
for image segmentation, Pattern Recognition, 29(5) (1996), 859-871.
[3] J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press,
NY. (1981)
[4] C. Clifton and D. Marks, Security and privacy implications of data mining, Workshop on
Data Mining and Knowledge Discovery, Montreal, Canada, (1996), 15–19.
[5] J. C. Da Silva, C. Giannella, R. Bhargava, H. Kargupta and M. Klusch, Distributed data
mining and agents, Engineering Applications of Artificial Intelligence, 18 (7) (2005), 791-
[6] W. Du and Z. Zhan, Building decision tree classifier on private data, Clifton, C., Estivill-
Castro, V. (Eds.), IEEE ICDM Workshop on Privacy, Security and Data Mining, 

Conferences in Research and Practice in Information Technology, Vol. 14, Maebashi
City, Japan, ACS, (2002), 1–8.
[7] T. Johnsten and V. V. Raghavan, A methodology for hiding knowledge in databases,
Clifton, C., Estivill-Castro, C. (Eds.), IEEE ICDM Workshop on Privacy, Security and
Data Mining, Conferences in Research and Practice in Information Technology, Vol.
14. Maebashi City, Japan, ACS, (2002), 9–17.
[8] H. Kargupta, L. Kun, S. Datta, J. Ryan and K. Sivakumar, Homeland security and
privacy sensitive data mining from multi-party distributed resources, Proc. 12th IEEE
International Conference on Fuzzy Systems, FUZZ '03, .Volume 2, May (2003), 25-28,
Vol. 2 (2003), 1257 – 1260.
[9] S. Merugu, and J. Ghosh, A privacy-sensitive approach to distributed clustering, Pattern
Recognition Letters, 26 (4) (2005), 399-410.
[10] B. Park and H. Kargupta, Distributed data mining: algorithms, systems, and applications, In:
Ye, N. (Ed.), The Handbook of Data Mining. Lawrence Erlbaum Associates, New
York, (2003), 341–358.
[11] W. Pedrycz, Algorithms of fuzzy clustering with partial supervision, Pattern Recognition
Letters, 3 (1985), 13 - 20.
[12] W. Pedrycz, and J. Waletzky, Fuzzy clustering with partial supervision, IEEE Trans. on
Systems, Man and Cybernetics, 5 (1997), 787-795.
[13] W. Pedrycz and J. Waletzky, Neural network front-ends in unsupervised learning, IEEE
Trans. on Neural Networks, 8 (1997), 390-401.
[14] W. Pedrycz, V. Loia and S. Senatore, P-FCM: A proximity-based clustering, Fuzzy Sets &
Systems, 148, (2004), 21-41.
[15] W. Pedrycz, Collaborative fuzzy clustering, Pattern Recognition Letters, 23(14)(2002),
[16] W. Pedrycz, Knowledge-Based Clustering: From Data to Information Granules, J. Wiley,
New York (2005).
[17] W. Pedrycz and F. Gomide, Fuzzy Systems Engineering: Toward Human-Centric
Computing, J. Wiley, NJ Hoboken, ( 2007).
[18] A. Strehl and J. Ghosh, Cluster ensembles—a knowledge reuse framework for combining
multiple partitions, Journal of Machine Learning Research, 3, (2002), 583–617.
[19] H. Timm, F. Klawonn and R. Kruse, An extension of partially supervised fuzzy cluster
analysis, Proc. Annual Meeting of the North American Fuzzy Information Processing
Society, NAFIPS, (2002), 63 –68.
[20] G. Tsoumakas, L. Angelis and I. Vlahavas, Clustering classifiers for knowledge discovery
from physically distributed databases, Data & Knowledge Engineering, 49(3) (2004), 223-
[21] V. S. Verykios, et al. State of the art in privacy preserving data mining, SIGMOID
Record, 33(1) (2004), 50-57.
[22] L. A. Zadeh, Toward a generalized theory of uncertainty (GTU) – an outline, Information
Sciences, 172(1-2) (2005), 1-40.