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By Carlos Dualibe

Fuzzy good judgment is a computational paradigm able to modelling the personal uncertainness of people. This wide-ranging booklet focuses in-depth at the VLSI CMOS implementation and alertness of programmable analogue Fuzzy good judgment Controllers following a mixed-signal philosophy.

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For instance, assume two complementary crisps sets, A and B, defined in the Universe of Discourse U={"the population of Louvain-la-Neuve"}: 2. 4 a) shows the characteristic functions for the two sets above. 4 b) shows the membership functions for AF and BF together with their intersection that has been performed by using the "min" operator as T-Norm. Notice that the intersection between the crisp sets A and B is the null set In contrast, the intersection between AF and BF is another, not null, fuzzy set that can be interpreted as: "the people of L-L-N that are neither young nor adult".

A design and optimization methodology suitable for Fuzzy Control is presented in [Godj97]. 12, which shows the block diagram of a Fuzzy Controller inserted in closed loop together with the Plant under control. 9. 12. It comprises a Data Base and a Rule Base. The first provides the linguistic variables, their term sets, the 2. Fuzzy Logic and Fuzzy Systems 33 membership functions shape and position, the inference method and the defuzzification method. e. a kind of "fuzzy inverse modeling"). Finally, a Learning or Tuning Algorithm adapts the parameters of the controller by minimizing, for instance, the RMSE (Root Mean Square Error) between the desired and actual outputs of the plant.

A network structure facilitates the computation of the error gradient vector for adapting the parameters of the controller. Hence, it can be tuned by applying the gradient descent algorithm based on some collection of input-output data [Verl92]. 13 shows an example of an ANFIS network for a 2-input, 1-output, 2-rule Zero-Order controller. We will summarize briefly the fuzzy operations performed at each layer: Layer 1: performs fuzzification. The outputs of the nodes at this layer are the degrees of membership of the inputs according to the defined input membership functions.

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