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Fuzzy Logic

Dinesh Ganotra. Fuzzy Logic. 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.

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Fuzzy Logic

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  1. Dinesh Ganotra Fuzzy Logic

  2. 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.

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

  4. Tipper problem

  5. 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.

  6. In fuzzy logic, the truth of any statement becomes a matter of degree. A fuzzy set admits the possibility of partial membership in it.

  7. 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]

  8. 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).

  9. Main functions in matlab for fuzzy Logic implementation • fuzzy filename • var = readfis('filename.fis')‏ • evalfis([input1 input2 ...], var)‏ • anfis(tranDat)% Last column is output

  10. 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

  11. [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.

  12. Mamdani and Sugeno fuzzy logic • Sugeno output membership functions are either linear or constant • ... • endless

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