Question is it warm in here
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yes fairly warm maybe a little no not really. Fuzzy Logic. Implication and Inference. Question: Is it warm in here?. Answer. IF room is warm THEN set cooling power to 500 watts. Fuzzy Logic. Implication and Inference. Fuzzy Inference. Premise. Consequence.

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Question: Is it warm in here?

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Question is it warm in here

yes

fairly warm

maybe

a little

no

not really

Fuzzy Logic

Implication and Inference

Question: Is it warm in here?

  • Answer

  • IF room is warmTHEN set cooling power to 500 watts


Fuzzy inference

Fuzzy Logic

Implication and Inference

Fuzzy 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


Terminologies

Fuzzy Logic

Fuzzy Logic

Terminologies

  • 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 membership function

Fuzzy Logic

Membership Function

Fuzzy Membership Function

  • Single-Valued (Singleton)

  • Trapezoidal

  • Triangular

  • Sigmoid

  • Gaussian

  • etc., as can be seen later in Fuzzy Toolbox


Fuzzy membership function tall people

Fuzzy Logic

Membership Function

Fuzzy Membership Function: Tall People

Degree ofMembership

FuzzyMembershipFunction

Fuzzy Universe


Fuzzy membership function around noon

Fuzzy Logic

Membership Function

Fuzzy Membership Function: Around Noon

Trapezoid

Triangular

Smooth trapezoid

Smooth triangular


Fuzzy set operations

Fuzzy Logic

Membership Function

A

B

Fuzzy Set Operations

Min-Max Operators

OR

AND

NOT


Fuzzy logic operators

Fuzzy Logic

Membership Function

Fuzzy Logic Operators

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 operators1

Fuzzy Logic

Membership Function

Fuzzy Logic Operators

NOT Operator

OR and AND Operators

Max

Min

Algebraic sum

Algebraic product

Bounded sum

Bounded product


Fuzzy logic operators2

Fuzzy Logic

Membership Function

Fuzzy Logic Operators

  • Relation between s-Norm and t-Norm:

de Morgan’s Law

Min-Max

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

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


Homework 6

Fuzzy Logic

Membership Function

Homework 6

  • 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”.


Homework 6a

Fuzzy Logic

Membership Function

Homework 6A

  • 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”.


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