Introduction to Neural Networks and Fuzzy Logic Lecture
- Slides: 13
Introduction to Neural Networks and Fuzzy Logic Lecture 9 Dr. -Ing. Erwin Sitompul President University http: //zitompul. wordpress. com 2 0 1 7 President University Erwin Sitompul NNFL 9/1
Fuzzy Logic Implication and Inference Question: Is it warm in here? n. Answer q q q yes fairly warm maybe a little no not really n IF room is warm THEN set cooling power to 500 watts President University Erwin Sitompul NNFL 9/2
Fuzzy Logic Implication and Inference Fuzzy Inference Premise Consequence n IF room is warm, THEN set cooling power to 500 watts. Measurement n The room temperature is 21 °C. n Set cooling at 280 watts. Action President University Erwin Sitompul NNFL 9/3
Fuzzy Logic Terminologies n Fuzzy Universe: range of all possible values to a chosen variable n Fuzzy Set: set with fuzzy boundaries n Fuzzy Membership Function: used to define fuzzy set n Fuzzy Set Operations: not, or, and n Fuzzy Logic Operators: the realization of set operation n Fuzzy Variable or Fuzzy Linguistic Value: variable assigned to fuzzy sets, such as: tall, high, fast n Fuzzy Linguistic Variable: variable that takes the value of certain fuzzy variable, such as: person, pressure, velocity n Fuzzy Rules: conditional statements that relates fuzzy sets President University Erwin Sitompul NNFL 9/4
Fuzzy Logic Membership Function Fuzzy Membership Function n Single-Valued (Singleton) n Trapezoidal n Triangular n Sigmoid n Gaussian n etc. , as can be seen later in Fuzzy Toolbox President University Erwin Sitompul NNFL 9/5
Fuzzy Logic Membership Function Fuzzy Membership Function: Tall People Degree of Membership Fuzzy Membership Function Fuzzy Universe President University Erwin Sitompul NNFL 9/6
Fuzzy Logic Membership Function Fuzzy Membership Function: Around Noon Trapezoid Triangular Smooth trapezoid Smooth triangular President University Erwin Sitompul NNFL 9/7
Fuzzy Logic Membership Function Fuzzy Set Operations A B Min-Max Operators OR AND NOT President University Erwin Sitompul NNFL 9/8
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 President University Erwin Sitompul NNFL 9/9
Fuzzy Logic Membership Function Fuzzy Logic Operators NOT Operator OR and AND Operators Max Min Algebraic sum Algebraic product Bounded sum Bounded product President University Erwin Sitompul NNFL 9/10
Fuzzy Logic Membership Function Fuzzy Logic Operators n Relation between s-Norm and t-Norm: de Morgan’s Law Min-Max Algebraic . . . . ? (Prove) Bounded. . . . ? (Prove) President University Erwin Sitompul NNFL 9/11
Fuzzy Logic Membership Function Homework 9 n The following membership functions are given: “Temperature is low” μTl(T), “Temperature is middle” μTm(T). n For all three possible realizations of FL-Operators (Min-Max, Algebraic, Bounded), draw the membership functions of: (i) “Temperature is low” AND “Temperature is middle”; (ii) “Temperature is low” OR “Temperature is middle”. President University Erwin Sitompul NNFL 9/12
Fuzzy Logic Membership Function Homework 9 A n The following membership functions are given: “Pressure is moderate” μPm(P), “Pressure is high” μPh(P). n 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”. n Deadline: Monday, 20 March 2017. President University Erwin Sitompul NNFL 9/13
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