Neural Net Applications in Fuzzy Systems

  • Hiroshi Kawamura
  • Akinori Tani
Part of the International Series on Microprocessor-Based and Intelligent Systems Engineering book series (ISCA, volume 11)


The concepts of fuzzy sets and fuzzy systems proposed by Zadeh xc18 xc19 have many possibilities of being applied to the description and analysis of this real fuzzy world. In the application of these conepts to knowledge engineering, there are two problems, i.e., learning of fuzzy knowledge and automatic inference of unknown variables. On the, other hand, one can identify any complex complex functions by means or perceptron-type neural networks xc12 and the back-propagation error method.

The purpose of this chapter is to propose some methods of neural network applications to fuzzy systems (and not of fuzzy system applications to neural networks (xc10). As mentioned above, the concept of neural networks is very useful for learning knowledge and automatic inference. In this chapter, besides usual neural networks, a couple of quasi-neural network methods are proposed.

In the field of engineering planning and design, evaluation and optimization are performed by using many kinds of variables (e.g., load, size, weight, strength, intensity, deformation, cost and so on) and constraints (e.g., design formula, mathematical equation, function, code, criterion and so on). Due to inevitable uncertainties, in general, these variables and constraints can be described with fuzzy sets and fuzzy relations cx17 xc18, respectively, which can include rationally usual crisp, deterministic and probabilistic expressions as special states.

As conditioned probabilities are used in probability systems, so conditioned fuzzy sets xc1 are used as states in fuzzy systems composed of inputs, states and outputs xc19. In engineering problems, such conditioned fuzzy sets which belong to fuzzy relations are very useful enough to discriminate uncertainties in variables from ones in constraints (or functions) xc3.

The final purpose of this paper is to propose a paradig, of intelligent and neural fuzzy networks in which learning, identification, evaluation and optimization can be performed for engineering planning and design by expanding fuzzy systems and employing a couple of models similar to neural networks xc10 .


Membership Function Fuzzy System Structural Safety Engineering Planning Fuzzy Relational Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Bellman, R.E. and Zadeh, L.A., “Decision-Making in a Fuzzy Environment,” Management Science, 17,4, pp.141–164; Dec. 1970.CrossRefMathSciNetGoogle Scholar
  2. [2]
    Cui, X., Yamada, M., Kawamura, H., and Tani, A., “Support System for Selecting Structural Planning Data of R/C Multi-Story Frames with Cantilever-Type Shear Walls,” Extended Abstracts of the IV-ICCCBE’91 Cconference, Tokyo, Japan, pp.263: July 1991.Google Scholar
  3. [3]
    Kawamura, H., Tani, A., Kawamura, M., Matsumoto, S., and Yamada, M., “A General Formulation of the Confluence Rule of Fuzzy Goal and Constraint and its Non-Numerical Maximization,” Proc., 3rd Fuzzy System Symposium, Osaka, Japan, pp.71–76: June 1987. (in Japanese)Google Scholar
  4. [4]
    Kawamura, H., Tani, A., Yamamoto, Y., and Yamada, M., “Application of Fuzzy Confluence Rule to Subjective Evaluations in Structural Design,” Iinternational Workshop on Fuzzy System Applications, Iizuka, Japan, pp.185–186: Aug. 1988.Google Scholar
  5. [5]
    Kawamura, H., and Yao, J.T.P., “Application of Fuzzy Systems Based on Conditioned Fuzzy Sets to Structural Engineering,” Journal of Structural Engineering, Vol.32B, pp.51–56: March 1990. (in Japanese)Google Scholar
  6. [6]
    Kawamura, H., Tani, A., Yamamoto, K., and Yamada, M., “Constitution of Intelligent Fuzzy Network by Frame Knowledge Representation,” Proc, International Conference on Fuzzy Logic & Neural Networks, Vol.1, Iizuka, Japan, pp.261–265: July 1990.Google Scholar
  7. [7]
    Kawamura, H., and Tani, A., “Multi-variable Fuzzy Identifier,” Proc, 6th Fuzzy System Symposium, Tokyo, Japan, pp.179–182: Sept.1990. (in Japanese)Google Scholar
  8. [8]
    Kawamura, H., Tani, A., Kambara, H., and Yamada, M., “Intelligent Fuzzy Network for Optimum Structural Planning and Design,” Proc., 7th Fuzzy System Symposium, Nagoya, Japan, pp.99–102: June 1991. (in Japanese)Google Scholar
  9. [9]
    Kawamura, H., Tani, A., and Kambara, H., “Aseismic Structural Planning System by Fuzzy Network,” Proc. 10th World Conference on Earthquake Engineering, Vol.10, Madrid, Spain, pp.6271–6275: July 1992.Google Scholar
  10. [10]
    Kawamura, H., Tani, A., “A Paradigm of Intelligent Fuzzy Networks,” Proc., The IEEE International Conference on Systems Engineering, Kobe, Japan, pp.159–164: Sept. 1992.Google Scholar
  11. [11]
    Papis, C.P. and Sugeno, M., “Fuzzy Relational Equations and the Inverse Problem,” Fuzzy Sets and Systems, 15, pp.79–90: 1985.CrossRefMathSciNetGoogle Scholar
  12. [12]
    Rosenblatt, F., “The Perceptron:A Probabilistic Model for Information Storage and Organization in the Brain,” Psychological Review, Vol.65, No.6, pp.386–408: 1958.CrossRefMathSciNetGoogle Scholar
  13. [13]
    Rumelhart, D.E., Hinton, G.E., and Williams, R.J., “Learning Representations by Back-propagation Errors,” Nature, 323–9, pp.533–536: Oct. 1986.CrossRefGoogle Scholar
  14. [14]
    Sanchez, E., “Resolution of Composite Fuzzy Relational Equations,” Information and Control, 30, pp.38–48: 1976.CrossRefMATHMathSciNetGoogle Scholar
  15. [15]
    Yamada, M., Kawamura, H., Tani, A., and Yamamoto, K., “A Determination Method of Hierarchy Models for Decision Making in Aseismic Structural Design by Fuzzy Confluence Rule,” Proc., The 12th Symposium on Computer Technology of Information, Systems and Applications, Kyoto, Japan, pp.223–228: Dec. 1989. (in Japanese)Google Scholar
  16. [16]
    Yamada, M., Kawamura, H., and Tani, A., “Research on Quantitative Formulation and Objective Determination Methods of Multi-Objective Decision Making Process in Aseismic Structural Design (Comparison between Fuzzy Confluence Rule and Neural Network),” Proc. of Annual Meeting, Structural Division, Airchtectural Institute of Japan, Kinki Branch, pp.161–164: May 1991. (in Japanese)Google Scholar
  17. [17]
    Yao, J.T.P, Safety and Reliability of Existing Structures, Pitmann Publ. Inc, Boston, London, Melbourne: 1985.Google Scholar
  18. [18]
    Zadeh, L.A.,“Fuzzy Sets,” Information and Control, Vol.8, pp.338–353: 1965.Google Scholar
  19. [19]
    Zadeh, L.A., “Toward a Theory of Fuzzy Systems,” in Aspects of Network and System Theory, (Eds. Kalman, R.E. and DeClaris, N.), Holt, Rinehart and Winster, Inc.: 1971.Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Hiroshi Kawamura
    • 1
  • Akinori Tani
    • 1
  1. 1.Department of Architecture and Civil Engineering Faculty of EngineeringKobe UniversityKobeJapan

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