Meaning of “fuzzy” Covered with fuzz; Of or resembling fuzz; Fuzzy Logic Introduction Meaning of “fuzzy” Covered with fuzz; Of or resembling fuzz; Not clear; indistinct A fuzzy recollection of past events. Not coherent; confused A fuzzy plan of action. Unclear, blurred, or distorted Some fuzzy pictures from a Russian radar probe.

4 Seasons 1 Membership 0.5 Time of the year Spring Summer Autumn Fuzzy Logic Introduction 4 Seasons 0.5 1 Time of the year Membership Spring Summer Autumn Winter

Tall Persons 1 : A person is tall 0 : A person is not tall Fuzzy Logic Introduction Tall Persons 1 : A person is tall 0 : A person is not tall

Room Temperature 1 : room is warm 0 : room is not warm Fuzzy Logic Introduction Room Temperature 1 : room is warm 0 : room is not warm Incorporation of human’s perception

Classical Sets young = { x  P | age(x) ≤ 20 } A=“young” Fuzzy Logic Set Definition Classical Sets young = { x  P | age(x) ≤ 20 } Characteristic function: A=“young” 1

Fuzzy Sets Classical Logic Fuzzy Logic Set Definition Fuzzy Sets Classical Logic Fuzzy Logic Element x whether belongs to set A or not at all: (x){0,1} Element x belongs to set A with a certain “degree of membership”: (x)[0,1] A=“young” 1 A=“young” 1

Fuzzy Sets Definition: Fuzzy Logic Set Definition Fuzzy Sets Definition: Fuzzy Set A = {(x,A(x)) | x  X, A(x)  [0,1]} is defined by a universe of discourse x where 0 ≤ x ≤ 100 and a membership function A where A(x)  [0,1] A=“young” 1 Membership function also called characteristic function

Some Definitions Support of a fuzzy set A Fuzzy Logic Set Definition Some Definitions Support of a fuzzy set A supp(A) = { x  X | A(x) > 0 } Core of a fuzzy set A core(A) = { x  X | A(x) = 1 } α-cut of a fuzzy set A Aα = { x  X | A(x)  α} x (x) 1 Alpha cuts usual for implementation in a computer α = 0.6

Fuzzy Logic Control (FLC) Fuzzy Logic Control (FLC) may be viewed as a branch of intelligent control which serves as an emulator of human decision-making behaviour which is approximate rather than exact. FLC uses the IF-THEN rules, similar to binary control (Programmable Logic Controller, PLC). Rule Format: Ri: IF x is Aj AND y is Bk THEN z is Cl Ri: IF x is Aj OR y is Bk THEN z is Cl

Fuzzy Logic Fuzzy Logic Operators Logic Operators

Boolean OR and Fuzzy OR Boolean OR Fuzzy OR Fuzzy Logic Fuzzy Logic Operators Boolean OR and Fuzzy OR Boolean OR Fuzzy OR

Boolean AND and Fuzzy AND Fuzzy Logic Fuzzy Logic Operators Boolean AND and Fuzzy AND Boolean AND Fuzzy AND

Example: Air Fan Conventional (On-Off) Control: Fuzzy Logic Fuzzy Logic Control Example: Air Fan Conventional (On-Off) Control: IF temperature > X °C, THEN run fan, ELSE stop fan. Fuzzy Control: IF temperature is hot, THEN run fan at full speed; IF temperature is warm, THEN run fan at moderate speed; IF temperature is comfortable, THEN maintain fan speed; IF temperature is cool, THEN slow fan; IF temperature is cold, THEN stop fan.

Example: Stopping A Car Fuzzy Logic Fuzzy Logic Control Example: Stopping A Car Break force Mass of the car Initial position Initial velocity

Example: Stopping A Car Fuzzy Logic Fuzzy Logic Control Example: Stopping A Car P-Control PD-Control With Kp = –240, the car will stop at the traffic light after 10 s. Choosing ζ = 1, Td = 1, Kp = 6000, the car will stop at the traffic light after 5 s.

Example: Stopping A Car Fuzzy Logic Fuzzy Logic Control Example: Stopping A Car Fuzzy Logic Control: IF distance is long AND approach is fast, THEN brake zero; IF distance is long AND approach is slow, THEN brake zero; IF distance is short AND approach is fast, THEN brake hard; IF distance is short AND approach is slow, THEN brake zero.

Fuzzy Membership Functions Fuzzy Logic Fuzzy Logic Control Fuzzy Membership Functions

Fuzzy Logic Fuzzy Logic Control Response