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Additional info for Design of Analog Fuzzy Logic Controllers in CMOS Technologies: Implementation, Test and Application
The meaning and the evaluation of a single rule and a set of rules were 2. Fuzzy Logic and Fuzzy Systems 37 focused. This lead to the description of the two most used Fuzzy Reasoning algorithms: Mamdani and Takagi-Sugeno. The methodology for design and optimization of Fuzzy Systems proposed by [Godj97] has been briefly introduced. It allows finding an optimal Fuzzy Controller in an iterative way. Beginning with the know-how provided by an expert the adaptation of the controller’s parameters is on-line performed under the supervision of a learning algorithm.
After a visual inspection of the function to approximate, we estimate in a first trial that the input space could be partitioned in nine clusters. So we initialize the controller with three membership functions per input equally distributed along the input domain of X and Y. We start the learning algorithm with all singletons at the consequents initialized at zero. e. 082. 15 shows the membership functions of input X before and after learning, the evolution of the RMSE and the obtained surface after 140 epochs.
In this text we call the latter as Complementary Fuzzy Membership Function (CFMF). 6) to each predefined Fuzzy Membership Function (FMF). 21) De Morgan’s law must be applied. For this purpose, a T-CoNorm (S-Norm) followed by complementation must be used rather than a direct T-Norm. n. 8. 21) resides on the fact that "max" operators are easier implemented than "min" operators with analog current-mode hardware. 2 Takagi-Sugeno’s If-Then Rules. To conclude this section dedicated to Fuzzy Rules, let us introduce the Takagi-Sugeno’s if-then rules model [SuYa93].