Fuzzy qualitative trigonometry
International Journal of Approximate Reasoning
New model for system behavior prediction based on belief rule based systems
Information Sciences: an International Journal
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Defines four types of fuzzy neurons and proposes the structure of a four-layer feedforward fuzzy neural network (FNN) and its associated learning algorithm. The proposed four-layer FNN performs well when used to recognize shifted and distorted training patterns. When an input pattern is provided, the network first fuzzifies this pattern and then computes the similarities of this pattern to all of the learned patterns. The network then reaches a conclusion by selecting the learned pattern with the highest similarity and gives a nonfuzzy output. The 26 English alphabets and the 10 Arabic numerals, each represented by 16×16 pixels, were used as original training patterns. In the simulation experiments, the original 36 exemplar patterns were shifted in eight directions by 1 pixel (6.25% to 8.84%) and 2 pixels (12.5% to 17.68%). After the FNN has been trained by the 36 exemplar patterns, the FNN can recall all of the learned patterns with 100% recognition rate. It can also recognize patterns shifted by 1 pixel in eight directions with 100% recognition rate and patterns shifted by 2 pixels in eight directions with an average recognition rate of 92.01%. After the FNN has been trained by the 36 exemplar patterns and 72 shifted patterns, it can recognize patterns shifted by 1 pixel with 100% recognition rate and patterns shifted by 2 pixels with an average recognition rate of 98.61%. The authors have also tested the FNN with 10 kinds of distorted patterns for each of the 36 exemplars. The FNN can recognize all of the distorted patterns with 100% recognition rate. The proposed FNN can also be adapted for applications in some other pattern recognition problems