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Artificial Intelligence Techniques

Artificial Intelligence Techniques. Knowledge Processing 2-MSc. Aims of session. To understand Fuzzy Logic Defuzzification. Introduction. Lofti Zadeh (1965) proposed Possibilistic Logic which became Fuzzy-Logic. Allows us to combine weighting factors with propositions. 0<=T(X)<=1.

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Artificial Intelligence Techniques

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  1. Artificial Intelligence Techniques Knowledge Processing 2-MSc

  2. Aims of session To understand • Fuzzy Logic • Defuzzification

  3. Introduction • Lofti Zadeh (1965) proposed Possibilistic Logic which became Fuzzy-Logic. • Allows us to combine weighting factors with propositions. • 0<=T(X)<=1

  4. Boolean v Fuzzy • Boolean Fuzzy T(X^Y) MIN(T(X),T(Y)) T(XvY) MAX(T(X),T(Y)) T(¬X) (1-T(X)) T(XY) MAX((1-T(X),T(Y)) Where X and Y are propositions Any Boolean expression can be converted to a fuzzy expression.

  5. t X Y Min(X,Y) MAX(X,Y) (1-X) MAX((1-X),Y) 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 1 0 0 1 1 1 1 0 1 So when truth values are 0 and 1 Fuzzy=Boolean Other rules such as De-Morgan’s Laws still apply

  6. Membership functions • A fuzzy set is a set whose membership function takes values between 0 and 1. • Example: Cold, Warm and Hot describe temperature we could define thresholds T1 and T2. • Starting at low temperature as the temperature rises to T1 the temperature becomes Warm. As the temperature rises to T2 the temperature becomes Hot.

  7. What is the problem? • Is there really a crisp change between the definitions?

  8. Answer • Change the shape of the membership function so it not so crisp. • Common one is a triangular functions that have some overlap. • At some temperatures it is possible to be a member of two different sets.

  9. Using the example from Johnson and Picton (1995)

  10. At 8 degrees it is a member of both COLD (0.7) and WARM (0.3) sets. • These are NOT necessarily probabilities, they are not so rigorously defined.

  11. Defuzzication • To calculate final setting need defuzzication rules, this often based around the ‘centre of gravity’ of shaded area. • Why do we need this?

  12. So back to the temperature measures the fuzzy membership can be combined using MIN, MAX and (1-T(X)) operations so IF-THEN can be used. • IF (temperature is COLD) THEN (heating on HIGH) • IF (temperature is WARM) THEN (heating on LOW) • So first rule heating is turned on to HIGH with a membership of 0.7.Second rule heating is turned on to LOW. • So membership can be represented by the heating memebership,

  13. Heater membership • Centre of gravity is point where area to left of the point=area to the right.

  14. Centre of Gravity

  15. Paradoxes and Fuzzy Sets • A useful feature is they can be built on the basis of minimal information and fine-tuned to be more consistent afterwards by observation. • Problem is (Hopgood’s Paradox) is that it is possible that ‘weak’ information can result in strong information on defuzzication.

  16. Not inverse • Defuzzication is not truly the inverse of fuzzification. • If you defuzzify fuzzy data you will often get distortion in the resulting values.

  17. References • Johnson J and Picton P (1995) Mechatronics : designing intelligent machines. - Vol.2 : concepts in artificial intelligence Oxford : Butterworth-Heinemann pg 175-187

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