A fuzzy neuron based upon maximum entropy ordered weighted averaging
There have been several interesting attempts to blend fuzzy set logic and neural networks. These include Shiue and Grondin , Yager , Taber and Deich , Kosko , Oden , and more recently Yamakawa and Tomoda  and Langheld and Goser . This paper extends the work of Yamakawa and Tomoda by employing Maximum Entropy Ordered Weighted Averaging (MEOWA) operations at the soma of a fuzzy neuron. The MEOWA is an extension by O'Hagan [6, 2] of Yager's [4, 5] Ordered Weighted Averaging (OWA) operators. The advantage of using the MEOWA operator in a fuzzy neuron is that a single type IC appears to be sufficient to build a neural pattern recognition system. Neural inputs and weights are fuzzy numbers rather than the usual scalar values of "standard" neural networks. Fuzzy logic operations replace the usual summing, dot product, and nonlinear "squashing" operations in the soma. Fuzzy neurons appear to be able to perform pattern recognition with reduced resolution inputs relative to standard neural networks: O(m) + O(n) vs. O(mn).
KeywordsFuzzy neural networks neural integrated circuits squashing function fuzzy logic operations aggregation theory ordered weighted averaging maximum entropy ordered weighted averaging membership functions character recognition
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- T. Yamakawa and S. Tomoda. (1989) A Fuzzy Neuron and Its Application to Pattern Recognition, In Proc. 3rd Ann. IFSA, 30–38, Univ. of Washington, Seattle, WA, August 1989.Google Scholar
- M. O'Hagan. (1988) Aggregating Template or Rule Antecedents in Real-Time Expert Systems with Fuzzy Set Logic. In Proc. 22nd Ann. Asilomar Conf. on Signals, Systems, and Computers, IEEE & Maple Press, 681–689, Pacific Grove, CA, October 31–November 2, 1988. Accepted for publication in IEEE Trans. on Syst., Man, and Cybernetics.Google Scholar
- L.C. Shiue and R.O. Grondin. (1987) On Designing Fuzzy Learning Neural-Automata. In Proc. ICNN, 2, 299–307, San Diego, CA, June 1987.Google Scholar
- R.R. Yager (1987) On the Aggregation of Processing Units in Neural Networks. In Proc. ICNN, 2, 327–333, San Diego, CA, June 1987.Google Scholar
- R.R. Yager. (1988) On Ordered Weighted Averaging Aggregation Operators in Multi-Criteria Decisions, Technical Report MII-705, Machine Intelligence Institute, Iona College, New Rochelle, NY, 1987 and in IEEE Trans. on Systems Man, and Cybernetics, 8,1, 183–190, Jan/Feb 1988.Google Scholar
- M. O'Hagan. (1987) Fuzzy Decision Aids. In Proc. 21st Ann. Asilomar Conf. on Signals, Systems, and Computers, IEEE and Maple Press, 2, 624–628, Pacific Grove, CA, Nov 1987.Google Scholar
- W.R. Taber and R. O. Deich. (1988) Fuzzy Sets and Neural Networks. In Proc. NASA 1988 First Joint Technology Workshop on Neural Networks and Fuzzy Logic, Houston, TX, May 1988.Google Scholar
- G. C. Oden. (1988) FuzzyProp: A Symbolic Superstrate for Connectionist Models. In Proc. ICNN, 1, 293–300, San Deigo, CA, July 1988.Google Scholar
- E. Langheld and K. Goser. (1990) Generalized Boolean Operations for Neural Networks. In Proc. IJNCC-90, 2, 159–162, Washington, DC, Jan. 15–19, 1990.Google Scholar
- B. Kosko. (1988) Fuzziness and Neural Networks. In Proc. 2nd Ann. IFSA, 5–7, Iizuka, Japan, August 20–24, 1988.Google Scholar
- M. Atkins. (1990) Sorting by Hopfield NET. In Proc. IJCNN-90, 2, 65–68, Washington, D.C., Jan. 15–19, 1990.Google Scholar