Defuzzification

Finally, a crisp value for OSUS (step 9 in Fig. 1) is computed via the height method of defuzzification,

OSUS = \frac{\sum_{\begin{array}{l} all fuzzy sets L \\ of OSUS \end{array}} y_{L} μ_{L} (OSUS)}{\sum_{\begin{array}{l} all fuzzy sets L \\ of OSUS \end{array}} μ_{L} (OSUS)}

where y_L is the peak value of the fuzzy set L—a value of OSUS for which the membership function of L is maximized.

For the example given in the previous section, only I, FH, and H are involved in the defuzzification. It is seen in Fig. 6c that y_I = 0.5, y_FH = 0.625, and y_H = 0.75. Therefore, the overall sustainability is given by

OSUS = \frac{0.5 \times 0.36 + 0.625 \times 0.58 + 0.75 \times 0.06}{0.36 + 0.58 + 0.06} = 0. 5875