72.

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Page 162

Each membership function shown above generates different membership grades. For instance, a trapezoidal membership function outputs a membership grade of 1 for a range of inputs s(i.e. 0≤|s−a|≤λ), while other membership functions allow only unique values of s (i.e. s=a) to hold the full membership value. As the distance between element s and the membership function centre c increases, the decreasing level of membership grade varies with different membership functions. Also, the greater the value of parameter λ the wider the range of s that is given a non-zero membership grade. Examples are shown in Figure 4.7. Here, two kinds of membership functions, triangular (Figure 4.7a and b based on Equation (4.27)) and trapezoidal (Figure 4.7c and d based on Equation (4.28)) are presented. Membership functions shown in (a) and (c) use the value λ=10, and can output non-zero membership grades for 0<s<20. Membership functions shown in (b) and (d) use the value λ=20, and both can thus output nonzero membership grades for 0<s<40. The areas of the trapezoidal membership functions that generate membership grades of 1 are shown as the shaded area of (c) and (d).

Figure 4.7 (a and b) Triangular membership functions, (c and d) Trapezoidal membership functions. See text for discussion.

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