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Fuzzy Set Representation for Small Integers and Pendulum Problem

Explore fuzzy set representation for small integers and the inverted pendulum problem using Figures 8.6 to 8.12 in this insightful study. Learn about fuzzy regions, input measures, Fuzzy Associative Matrix (FAM), and crisp outputs.

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Fuzzy Set Representation for Small Integers and Pendulum Problem

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  1. Figure 8.6: The fuzzy set representation for “small integers.” Figure 8.7 A fuzzy set representation for the sets short, median, and tall males.

  2. Figure 8.8: The inverted pendulum and the angle  and d/dt input values.

  3. Figure 8.9: The fuzzy regions for the input values  (a) and d/dt (b). Figure 8.10 The fuzzy regions of the output value u, indicating the movement of the pendulum base.

  4. Figure 8.11: The fuzzification of the input measures x1=1, x2 = -4.

  5. Figure 8.12: The Fuzzy Associative Matrix (FAM) for the pendulum problem. The input values are on the left and top.

  6. The fuzzy consequents(a) and their union (b). The centroid of the union (-2) is the crisp output.

  7. Minimum of their measures is taken as the measure of the rule result:

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