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Question: Is it warm in here?PowerPoint Presentation

Question: Is it warm in here?

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Question: Is it warm in here?

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yes

fairly warm

maybe

a little

no

not really

Fuzzy Logic

Implication and Inference

- Answer

- IF room is warmTHEN set cooling power to 500 watts

Fuzzy Logic

Implication and Inference

Premise

Consequence

- IF room is warm,THEN set cooling power to 500 watts.

Measurement

- The room temperature is 21 °C.

- Set cooling at 280 watts.

Action

Fuzzy Logic

Fuzzy Logic

- Fuzzy Universe: range of all possible values to a chosen variable
- Fuzzy Set: set with fuzzy boundaries
- Fuzzy Membership Function: used to define fuzzy set
- Fuzzy Set Operations: not, or, and
- Fuzzy Logic Operators: the realization of set operation
- Fuzzy Variable or Fuzzy Linguistic Value: variable assigned to fuzzy sets, such as: tall, high, fast
- Fuzzy Linguistic Variable: variable that takes the value of certain fuzzy variable, such as: person, pressure, velocity
- Fuzzy Rules: conditional statements that relates fuzzy sets

Fuzzy Logic

Membership Function

- Single-Valued (Singleton)
- Trapezoidal
- Triangular
- Sigmoid
- Gaussian
- etc., as can be seen later in Fuzzy Toolbox

Fuzzy Logic

Membership Function

Degree ofMembership

FuzzyMembershipFunction

Fuzzy Universe

Fuzzy Logic

Membership Function

Trapezoid

Triangular

Smooth trapezoid

Smooth triangular

Fuzzy Logic

Membership Function

A

B

Min-Max Operators

OR

AND

NOT

Fuzzy Logic

Membership Function

s-Norm: is monotonous associative operator with

t-Norm: is monotonous associative operator with

FL-OR must resemble s-Norm

FL-AND must resemble t-Norm

Monotony

Associativity

Fuzzy Logic

Membership Function

NOT Operator

OR and AND Operators

Max

Min

Algebraic sum

Algebraic product

Bounded sum

Bounded product

Fuzzy Logic

Membership Function

- Relation between s-Norm and t-Norm:

de Morgan’s Law

Min-Max

Algebraic ........? (Prove)

Bounded........? (Prove)

Fuzzy Logic

Membership Function

- The following membership functions are given:“Temperature is low” μTl(T),“Temperature is middle” μTm(T).

- For all three possible realizations of FL-Operators (Min-Max, Algebraic, Bounded), draw the membership functions of:(i) “Temperature is low” AND “Temperature ismiddle”;(ii)“Temperature is low” OR “Temperature is middle”.

Fuzzy Logic

Membership Function

- The following membership functions are given:“Pressure is moderate” μPm(P),“Pressure is high” μPh(P).

- For all three possible realizations of FL-Operators (Min-Max, Algebraic, Bounded), draw the membership functions of:(i) “Pressure is moderate” AND “Pressure is not high”;(ii)“Pressure is not moderate” OR “Pressure is high”.