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JACIII Vol.13 No.5 pp. 520-528
doi: 10.20965/jaciii.2009.p0520
(2009)

Paper:

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A Granular Unified Min-Max Fuzzy-Neuro Framework for Learning Fuzzy Systems

Mokhtar Beldjehem

Sainte Anne University, 1589 Walnut Street Halifax, Nova Scotia, B3H 3S1, Canada

Received:
September 19, 2008
Accepted:
February 21, 2009
Published:
September 20, 2009
Creative Commons License
Keywords:
fuzzy weighted rules, granular fuzzy-neuro possibilistic model, approximation of Min-Max relational equations
Abstract
We propose a novel computational granular unified framework that is cognitively motivated for learning if-then fuzzy weighted rules by using a hybrid neuro-fuzzy or fuzzy-neuro possibilistic model appropriately crafted as a means to automatically extract or learn fuzzy rules from only input-output examples by integrating some useful concepts from the human cognitive processes and adding some interesting granular functionalities. This learning scheme uses an exhaustive search over the fuzzy partitions of involved variables, automatic fuzzy hypotheses generation, formulation and testing, and approximation procedure of Min-Max relational equations. The main idea is to start learning from coarse fuzzy partitions of the involved variables (both input and output) and proceed progressively toward fine-grained partitions until finding the appropriate partitions that fit the data. According to the complexity of the problem at hand, it learns the whole structure of the fuzzy system, i.e. conjointly appropriate fuzzy partitions, appropriate fuzzy rules, their number and their associated membership functions.
Cite this article as:
M. Beldjehem, “A Granular Unified Min-Max Fuzzy-Neuro Framework for Learning Fuzzy Systems,” J. Adv. Comput. Intell. Intell. Inform., Vol.13 No.5, pp. 520-528, 2009.
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References
  1. [1] A. Newell and H. Simon, “Human Problem Solving, Englewood Cliffs,” NJ: Prentice Hall, 1972.
  2. [2] L. A. Zadeh, “Toward a theory of fuzzy systems,” in : R. E. Kalman, N. Declaris, Eds., Aspects of Network and System Theory (Holt, Rinehart and Winston, New York), pp. 209-245, 1971.
  3. [3] L. A. Zadeh, “A theory of approximate reasoning,” in Machine Intelligence 9 (J.E. Hayes et al.; Eds), Elsevier, pp. 149-194, 1979.
  4. [4] L. A. Zadeh, “A theory of commonsense knowledge,” in Aspect of Vagueness (H.J. Skala, S. Termini and E. Trillas, Eds), Dodrecht: Reidel, pp. 257-295, 1984.
  5. [5] L. A. Zadeh, “A new AI: Toward computational theory of perceptions,” AAAI Magazine 22, No.1, pp. 73-84, Springer, 2001.
  6. [6] L. A. Zadeh, “Fuzzy sets,” Info. Control 89, pp. 338-353, 1965.
  7. [7] L. A. Zadeh, “Outline of a new approach to the analysis of complex systems and decision processes,” IEEE Trans. Syst. Man Cybernet, 3, pp. 28-44, 1973.
  8. [8] L. A. Zadeh, “Fuzzy sets as a basis for a theory of possibility,” Fuzzy sets and syst. 1, pp. 3-28, 1978.
  9. [9] L. A. Zadeh, “Fuzzy logic neural networks, and soft computing,” Communications of the ACM 37, pp. 77-84, 1994.
  10. [10] M. Beldjehem, “A Contribution to the Conception of Hybrid Fuzzy-Neuro Systems by Approximation of Min-Max Fuzzy Relational Systems: the Fennec System,” Ph.D. Thesis in Computer Science and Software Engineering, Université de la Mediterannée, Aix- Marseille II, 1993.
  11. [11] M. Beldjehem, “Fennec, un générateur de systèmes neuro-flous,” in Proc. les Actes des Applications des Ensembles Flous, Nimes, France, pp. 209-218, 1993 (in French).
  12. [12] M. Beldjehem, “Le système fennec,” in Electronic BUSEFAL 55, pp. 95-104, 1993 (in French).
  13. [13] M. Beldjehem, “The fennec system,” in Proc. ACM Symposium on Applied Computing (SAC), Track on fuzzy logic in Applications, pp. 126-130, Phoenix, AZ (March), 1994.
  14. [14] M. Beldjehem, “Machine Learning based on the possibilistic-neuro hybrid approach: design and implementation,” in Electronic BUSEFAL 87, pp. 95-104, 2002.
  15. [15] M. Beldjehem, “Learning IF-THEN Fuzzy Weighted Rules,” in Proc. Int. Conf. of Computational intelligence, Nicosia, North Cyprus, 2002.
  16. [16] M. Beldjehem, “Validation of Hybrid MinMax Fuzzy-Neuro Systems,” in Proc. Int. Conf. of NAFIPS, Montreal, 2006.
  17. [17] M. Beldjehem, “Towards a Validation Theory of Hybrid MinMax Fuzzy-Neuro Systems,” in Proc. the WSEAS Int. Conf., Sofia, 2008.
  18. [18] M. Beldjehem, “A Validation Theory of Hybrid MinMax Fuzzy-Neuro Systems,” in Proc. the CIMSA Int. Conf., Istambul, 2008.
  19. [19] R.Yager and L. A Zadeh, “Fuzzy Sets, Neural Networks and Soft Computing,” Van Nostrand Reinhold: New York, 1994.
  20. [20] N. K. Sinha and M. Gupta (Eds.), “Soft Computing and Intelligent Systems: Theory and Applications,” Academic Press, New York, 1999.
  21. [21] R. Yager, “Fuzzy Set and Possibility Theory: Recent Developments,” Pergamon Press: New York, 1986.
  22. [22] S. K. Pal and A. Ghosh (Eds.), “Soft Computing in Image Processing,” Physica-Verlag, Heidelberg, 2000.
  23. [23] L. A. Zadeh, ”Fuzzy sets and information granulation,” in Advances in Fuzzy Set Theory and Applications, in M. Gupta, R. K. Ragade, R. R. Yager (Eds.), North-Holland Publishing Company, pp. 3-18, 1976.
  24. [24] R. Bellman, R. Kalaba, and L. Zadeh, “Abstraction and Pattern Classification,” J. Math. Anal. Appl. 13, pp. 1-7, 1966.
  25. [25] F. Giunchglia and T. Walsh, “A theory of abstraction,” Artificial Intelligence 56, pp. 323-390, 1992.
  26. [26] J. R. Hobbs “Granularity, Proc. of the 9th Int. Joint Conf. on Artificial Intelligence,” pp. 432-435, 1985.
  27. [27] D. Marr, “Vision, A Computational Investigation into Human Representation and Processing of Visual Information,” Freeman W. H. and Company, San Fransisco, 1982.
  28. [28] C. L. Foster, “Algorithms,” Abstraction and Implementation: Levels of details in cognitives sciences, Academic Press, London, 1992.
  29. [29] T. Y. Liu, Y. Y. Yao, and L. A. Zadeh, “Data Mining, Rough Sets and Granular Computing,” Physica-Verlag, Heidelberg, 2002.
  30. [30] Y. Y. Yao, “Granular computing: basic issues and possible solutions,” Proc. of the 5th Joint Conf. on Information Sciences, pp. 186-189, 2000.
  31. [31] W. Pedrycz (Ed.), “Granular Computing: An emerging paradigm,” Springer, Series: Studies in Fuzziness and Soft Computing 70, 2001.
  32. [32] L. A. Zadeh, “Some reflections on soft computing, granular computing and their roles in the conception, design and utilization of information / intelligent systems,” Soft Computing 2, pp. 23-25, 1998.
  33. [33] D. Dubois and H. Prade, “Possibility Theory: An Approach to Computerized Processing of Uncertainty,” Plenum Press, New York, USA, 1988.
  34. [34] W. Olaf, “Possibility Theory with Application to Data Analysis,” John Wiley & Son inc., 1998.
  35. [35] G. Miller, “The magical number seven, plus or minus two,” The Psychological Review 63, pp. 81-97, 1956.
  36. [36] M. Cayrol, H. Farreny, and H. Prade, “Fuzzy Pattern Matching,” Kybernetics 11, pp. 103-116, 1982.
  37. [37] D. Dubois, H. Prade, and C. Testemale, “Weighted fuzzy pattern matching,” Fuzzy sets and systems 28, pp. 313-331, 1988.
  38. [38] R. Yager “On the interpretation of Fuzzy If-Then Rules,” Applied Intelligence 6, pp. 141-151, 1996.
  39. [39] C. P. Pappis, “Value approximation of fuzzy systems variable,” Fuzzy sets and systems 39, pp. 111-115, 1991.
  40. [40] A. Dinola, S. Sessa, and W. Pedrycz, “Fuzzy Relation Equations and Their Applications To Knowledge Engineering,” Kluwer Acdemic Publisherss, Dordrecht, NL, 1989.
  41. [41] O. Cordon, F. Herrera, F. Hoffman, and L. Magdalena, “Genetic Fuzzy System,” Evolutionary Tuning and Learning of Fuzzy Knowledge Bases, Worlds Scientific, 2001.
  42. [42] W. Pedrycz (Ed.), “Fuzzy Evolutionary Computation,” Kluwer Academic Publishers, 1997.
  43. [43] L. A. Zadeh, “Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic,” Fuzzy Sets and Systems, 19, pp. 111-127, 1997.
  44. [44] L. A. Zadeh, “Soft Computing, Fuzzy Logic and Recognition Technology,” In Proc. IEEE Int. Conf. Fuzzy Syst., Anchorage, AK, pp. 1678-1679, 1998.
  45. [45] M. Gupta, L. Jin, and N. Homma, “Static and Dynamic Neural Networks: From Fundamentals to Advanced Theory,” John Wiley and Son Inc., New York, 2002.

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