A Journalist's Guide to Islam by Gordon Legge

By Gordon Legge

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For instance, if the third 32 Recurrent Neural Networks and Soft Computing input is ρ , then the entries in the third row of Bc should all be positive. Similarly, if the first output is the velocity correction vinc then the first column of Woc can take both negative /positive small values to allow the ANN to increase or decrease the robot speed while avoiding instability. Fig. 5. 5 Training phase To train the ANN, the following objective function is minimized: objg = 1 Np Np K i   ρip p= 1 i= 1 (10) where ‘ ρip ’ is the distance between the desired location on the pth path and the corresponding robot's actual location at the ith time instant, K i is the number of points along the path to be tracked and N p is the number of paths used in training.

7). Thus, the proposed modifications to conventional ANNs succeeded in producing an improved ANFIS system capable of outperforming both conventional ANNs and ANFIS for problems where the desired ANN output is not known a priori (like in the path tracking case study). 46 Recurrent Neural Networks and Soft Computing Fig. 14. Architecture of a typical ANFIS system for a 2 inputs single output example A Framework for Bridging the Gap Between Symbolic and Non-Symbolic AI 47 Fig. 15. Shows the results for using conventional ANNs and ANFIS instead of the proposed formulation for case B.

The membership function of a  R is  a ( x )  1, if x  a and  a ( x )  0 if x  a . Hence if a  0 we have the following 1 x  0 0 x  0. 1 Definition For A and B  E, define the ranking of A and B by saying A  B iff A  B iff A  B iff d( A, 0 )  d( B, 0 ), d( A, 0 )  d( B, 0 ), d( A, 0 )  d( B, 0 ). 2 Property Suppose A and B  E , are arbitrary, therefore If A  B then A  B. If B  A and LA1 (r )2  RA1 (r )2  LB1 (r )2  RB1 (r )2 for all r   0,1 then B  A. 1/2 (20) If A  B it is not necessary that A  B .

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