Introduction to Neural Networks and Fuzzy Logic Lecture

Introduction to Neural Networks and Fuzzy Logic Lecture 8 Dr. -Ing. Erwin Sitompul President University http: //zitompul. wordpress. com 2 0 1 3 President University Erwin Sitompul NNFL 8/1

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 8/2

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 8/3

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 8/4

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 8/5

Fuzzy Logic Membership Function Fuzzy Membership Function: Tall People Degree of Membership Fuzzy Membership Function Fuzzy Universe President University Erwin Sitompul NNFL 8/6

Fuzzy Logic Membership Function Fuzzy Membership Function: Around Noon Trapezoid Triangular Smooth trapezoid Smooth triangular President University Erwin Sitompul NNFL 8/7

Fuzzy Logic Membership Function Fuzzy Set Operations A B Min-Max Operators OR AND NOT President University Erwin Sitompul NNFL 8/8

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 8/9

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 8/10

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 8/11

Fuzzy Logic Membership Function Homework 6 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 8/12

Fuzzy Logic Membership Function Homework 6 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”. President University Erwin Sitompul NNFL 8/13