Machine Learning and Artificial Intelligence-Based Approaches - Hydrological Data Driven Modelling - page 93

Fig. 4.13 Mamdani FIS with crisp flood discharge and river stage crisp inputs

rule and the output membership function, (5) establishing output distribution
through combination of consequences, and (6) crisp outputs through defuzzi cation

of output distribution. An example of a Mamdani fuzzy inference system is shown
in Fig. 4.13 .
Fuzzy rules are a collection of linguistic statements which describe how FIS
make decisions based on inputs. As an example: in a

flood warning system:

If ð Water Level 7 m and 2mm

\ ¼

Rainfall 3mm Þ Then Issue Flood Alert

\ \

ðÞ low ð medium Þ

If ð 7m

\ ¼

Water Level 10 m and 3 mm

\ ¼

Rainfall 5mm Þ Then Issue Flood Warning

\ \

ð medium Þ ð medium Þ

If ð Water Level [ ¼ 10m and Rainfall [ ¼ 5mm Þ Then Issue Severe Flood Warning

high

ð Þ ð Þ

high

In Fig. 4.13 , a crisp output value r is obtained in a process known as defuzz-

i cation using distinct defuzzifying equations.

Another popular fuzzy framework is a Sugeno fuzzy model which is also known
as the Takagi

Kang method of fuzzy inference. The main difference from
Mamdani fuzzy is that Sugeno inference system doesn

Sugeno

- -

' t have proper output