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## 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 warmTHEN 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 Logic**Membership Function Fuzzy Membership Function • Single-Valued (Singleton) • Trapezoidal • Triangular • Sigmoid • Gaussian • etc., as can be seen later in Fuzzy Toolbox**Fuzzy Logic**Membership Function Fuzzy Membership Function: Tall People Degree ofMembership FuzzyMembershipFunction Fuzzy Universe**Fuzzy Logic**Membership Function Fuzzy Membership Function: Around Noon Trapezoid Triangular Smooth trapezoid Smooth triangular**Fuzzy Logic**Membership Function A B Fuzzy Set Operations Min-Max Operators OR AND NOT**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**Membership Function Fuzzy Logic Operators NOT Operator OR and AND Operators Max Min Algebraic sum Algebraic product Bounded sum Bounded product**Fuzzy Logic**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 7 • 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”.**Fuzzy Logic**Membership Function Homework 7A • 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”.