Fuzzy Logic

Dinesh Ganotra

What could go in the black box? Any number of things: fuzzy systems, linear systems, expert systems, neural networks, differential equations, interpolated multidimensional lookup tables, or even a spiritual advisor.

In almost every case you can build the same product without fuzzy logic, but fuzzy is faster

and cheaper.

Tipper problem

Classical or normal sets wouldn't tolerate this kind of thing. Either you're in or you're out. Human experience suggests something different, though: fence sitting is a

part of life.

In fuzzy logic, the truth of any statement becomes a matter of degree.

A fuzzy set admits the possibility of partial membership in it.

Fuzzy Logic

AND(A,B) Min(A,B) OR (A,B) Max(A,B) NOT(A) 1-A

Membership function Set [1 3 5] MF[0.1 0.9 0.5]

Q: Is Saturday a weekend day? A: 1 (yes, or true) Q: Is Tuesday a weekend day? A: 0 (no, or false) Q: Is Friday a weekend day? A: 0.8 (for the most part yes, but not completely) Q: Is Sunday a weekend day? A: 0.95 (yes, but not quite as much as Saturday).

Main functions in matlab for fuzzy Logic implementation

fuzzy filename var = readfis('filename.fis') evalfis([input1 input2 ...], var)

anfis(tranDat)% Last column is output

F V M 1 1 40 2 5 45 5 5 50 10 10 95 9 9 93 9 8 92 9 7 85 8 9 86 2 3 42 1 10 80 10 1 80

02

46

810

0

5

1020

40

60

80

100

vivafi le

Pra

c M

arks

[center,U,obj_fcn] = fcm(data,cluster_n)

The membership function matrix U contains the grade of membership of each DATA point in each cluster.

Mamdani and Sugeno fuzzy logic

Sugeno output membership functions are either linear or constant

...

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