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

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

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 of Membership Fuzzy Membership Function 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 Min-Max Operators OR AND NOT Fuzzy Logic Membership Function Fuzzy Set Operations A B Min-Max Operators OR AND NOT

FL-OR must resemble s-Norm FL-AND must resemble t-Norm 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 Operators NOT Operator OR and AND Operators Max Min Membership Function Fuzzy Logic Operators NOT Operator OR and AND Operators Max Min Algebraic sum Algebraic product Bounded sum Bounded product

Fuzzy Logic Operators Relation between s-Norm and t-Norm: Membership Function Fuzzy Logic Operators Relation between s-Norm and t-Norm: de Morgan’s Law Min-Max Algebraic ........? (Prove) Bounded ........? (Prove)

Fuzzy Logic Membership Function Homework 9 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 is middle”; (ii) “Temperature is low” OR “Temperature is middle”.

Homework 9A Deadline: Monday, 20 March 2017. Fuzzy Logic Membership Function Homework 9A 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”. Deadline: Monday, 20 March 2017.