Lecture 8 Introduction to Neural Networks and Fuzzy Logic President UniversityErwin SitompulNNFL 8/1 Dr.-Ing. Erwin Sitompul President University

President UniversityErwin SitompulNNFL 8/2 Question: Is it warm in here?  yes  fairly warm  maybe  a little  no  not really Implication and InferenceFuzzy Logic Answer IF room is warm THEN set cooling power to 500 watts

President UniversityErwin SitompulNNFL 8/3 Fuzzy Inference Implication and InferenceFuzzy Logic IF room is warm, THEN set cooling power to 500 watts. Premise Consequence Measurement The room temperature is 21 °C. Set cooling at 280 watts. Action

President UniversityErwin SitompulNNFL 8/4 Terminologies 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

President UniversityErwin SitompulNNFL 8/5 Fuzzy Membership Function Fuzzy Logic Single-Valued (Singleton) Trapezoidal Triangular Sigmoid Gaussian etc., as can be seen later in Fuzzy Toolbox Membership Function

President UniversityErwin SitompulNNFL 8/6 Fuzzy Membership Function: Tall People Membership FunctionFuzzy Logic Fuzzy Membership Function Fuzzy Universe Degree of Membership

President UniversityErwin SitompulNNFL 8/7 Fuzzy Membership Function: Around Noon Trapezoid Triangular Smooth trapezoid Smooth triangular Membership FunctionFuzzy Logic

President UniversityErwin SitompulNNFL 8/8 AB Min-Max Operators OR AND NOT Fuzzy Set Operations Membership FunctionFuzzy Logic

President UniversityErwin SitompulNNFL 8/9 t-Norm: is monotonous associative operator with s-Norm: is monotonous associative operator with FL-AND must resemble t-NormFL-OR must resemble s-Norm Associativity Monotony Membership FunctionFuzzy Logic Fuzzy Logic Operators

President UniversityErwin SitompulNNFL 8/10 NOT Operator OR and AND Operators Min Max Algebraic product Algebraic sum Bounded sum Bounded product Fuzzy Logic Operators Membership FunctionFuzzy Logic

President UniversityErwin SitompulNNFL 8/11 de Morgan’s Law Min-Max Algebraic ? (Prove) Bounded ? (Prove) Membership FunctionFuzzy Logic Fuzzy Logic Operators Relation between s-Norm and t-Norm:

President UniversityErwin SitompulNNFL 8/12 The following membership functions are given: “Temperature is low” μ Tl (T), “Temperature is middle” μ Tm (T). 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”. Membership FunctionFuzzy Logic Homework 6

President UniversityErwin SitompulNNFL 8/13 Membership FunctionFuzzy Logic Homework 6A The following membership functions are given: “Pressure is moderate” μ Pm (P), “Pressure is high” μ Ph (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”.