73.

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The resulting fuzzy partitions on one-dimensional space using the membership functions shown in Equations (4.26) to (4.29) alone are illustrated in Figure 4.8a. Note that the shape of the membership function and the size of overlapped area may vary. Besides using the same membership function to partition the space, one may also perform fuzzy partitions using combinations of different membership functions. The selection of membership function and the width of each fuzzy subspace are certainly case dependent.

Figure 4.8b shows an example of partitioning the input space. Here we take a simple problem, that of distinguishing between hot and warm water, and we use one monotonic, one triangular and one trapezoidal membership

Figure 4.8 (a) Partitioning one-dimensional space into fuzzy subspaces using a single fuzzy membership function, (b) The fuzzy partitions to deal with the problem of distinguishing hot, warm and cold water.

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