82.

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Page 171

Figure 4.13 (a) Procedure for the construction of fuzzy rule for each fuzzy subspace ij. (b) Procedure for classifying the image.

(4.39) (thus k=2, λ=1, a₁=0, a₂=1). If we use two training pixels, with one having values (0.7, 0.8) for class 1 and the other containing the value (0.5, 0.4) for class 2, the resulting parameters using Equations (4.38), (4.39), and the procedures shown in Figure 4.13a are shown in Table 4.1. The fuzzy rule for subspace i=1, j=1 can therefore be determined as:

IF s1 is in A₁ and s2 is in A₁

THEN pixel s belongs to class 2 with strength 0.43

The remaining three rules for fuzzy subspaces ij=12, 21 and 22 can be inferred in a similar manner.

After class labels c_ij and strengths w_ij in the rule have been determined, a rule for the fuzzy subspace ij is completely specified. The resulting rule base can be applied to classify the image in terms of the procedure illustrated in Figure 4.13b (Ishibuchi et al., 1992, 1995). When an unknown

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