Learning by fuzzified neural networks

Abstract We derive a general learning algorithm for training a fuzzified feedforward neural networks that has fuzzy inputs, fuzzy targets, and fuzzy conncetion weights. The derived algorithm is applicable to the learning of fuzzy connection weights with various shapes such as triangular and trapezoid. First we briefly describe how a feedforward neural network can be fuzzified. Inputs, targets, and connection weights in the fiuzzified neural network can be fuzzy numbers. Next we define a cost function that measures the differences between a fuzzy target vector and an actual fuzzy output vector. Then we derive a learning algorithm from the cost function for adjusting fuzzy connection weights. Finally we show some results of computer simulations.

[1]  Hisao Ishibuchi,et al.  Fuzzy neural networks with fuzzy weights and fuzzy biases , 1993, IEEE International Conference on Neural Networks.

[2]  J. Buckley,et al.  Fuzzy neural networks: a survey , 1994 .

[3]  James J. Buckley,et al.  Can fuzzy neural nets approximate continuous fuzzy functions , 1994 .

[4]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[5]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[6]  James J. Buckley.  Training a fuzzy neural net , 1994, NAFIPS/IFIS/NASA '94. Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference. The Industrial Fuzzy Control and Intellige.

[7]  Hideo Tanaka,et al.  Fuzzy regression analysis by fuzzy neural networks and its application , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[8]  Madan M. Gupta,et al.  Introduction to Fuzzy Arithmetic , 1991 .

[9]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[10]  Hisao Ishibuchi,et al.  Neural networks that learn from fuzzy if-then rules , 1993, IEEE Trans. Fuzzy Syst..

[11]  Hideo Tanaka,et al.  A fuzzy neural network with trapezoid fuzzy weights , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[12]  G. Alefeld,et al.  Introduction to Interval Computation , 1983 .

[13]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning - II , 1975, Inf. Sci..

[14]  Hisao Ishibuchi,et al.  Interpolation of fuzzy if-then rules by neural networks , 1994, Int. J. Approx. Reason..

[15]  Hisao Ishibuchi,et al.  Neural-network-based diagnosis systems for incomplete data with missing inputs , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).

[16]  H. Ishibuchi,et al.  A learning algorithm of fuzzy neural networks with triangular fuzzy weights , 1995 .

[17]  L. A. ZADEH,et al.  The concept of a linguistic variable and its application to approximate reasoning - I , 1975, Inf. Sci..

[18]  Kevin D. Reilly,et al.  Genetic learning algorithms for fuzzy neural nets , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[19]  James J. Buckley,et al.  Fuzzy neural network with fuzzy signals and weights , 1993, Int. J. Intell. Syst..