lecture 7

Fuzzy logic

1. Fuzzy logic: a computational approach centered on the idea of ‘degrees of truth’ rather than the black/white true or false approach of most systems.
2. Fuzzy membership function: permit individuals to be partial members of different, overlapping sets( crossover point: the point where the grade of membership is 0.5 )

Left sigmoidal: 需要两个参数，表示下降

Sigmoidal or triangular function：需要三个参数，表示大概

Trapezoidal-shaped：需要四个参数，表示中等

Right trapezoidal function：需要两个参数，表示增加

1. Fuzzy operators:

And: The output map is controlled by the smallest fuzzy membership value at each location.

 

Or: Output membership is controlled by the maximum value of input maps

 

Fuzzy Algebraic Product: output总是小于等于最小的FM，所有FM的值都参与

Fuzzy Algebraic Sum: sum of 0.75, 0.5 = 1-(1-0.75)*(1-0.5) = 0.875，结果总是比最大的还大