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 8 President University Erwin Sitompul NNFL 8/1

Fuzzy Logic Introduction Meaning of “fuzzy”, Definition of Fuzzy Logic n Covered with fuzz; n Of or resembling fuzz; n Not clear; indistinct A fuzzy recollection of past events. n Not coherent; confused A fuzzy plan of action. n Unclear, blurred, or distorted Some fuzzy pictures from a Russian radar probe. n Fuzzy logic: a form of knowledge representation suitable for notions that cannot be defined precisely, but depend upon their contexts, it deals with reasoning that is approximate rather than fixed and exact. President University Erwin Sitompul NNFL 8/2

Fuzzy Logic Introduction Origins of Fuzzy Logic n The earliest record can be traced back as far as to the ancient Greece period n Lotfi Zadeh (1965) The first to publish ideas of fuzzy logic n Toshire Terano (1972) The first to organize a working group of fuzzy system n F. L. Smidth et. al. The first to market fuzzy expert system President University Erwin Sitompul NNFL 8/3

Fuzzy Logic Introduction 4 Seasons Membership 1 Spring Summer Autumn Winter 0. 5 0 Time of the year President University Erwin Sitompul NNFL 8/4

Fuzzy Logic Introduction Tall Persons 1 : A person is tall 0 : A person is not tall President University Erwin Sitompul NNFL 8/5

Fuzzy Logic Introduction Room Temperature 1 : room is warm 0 : room is not warm Incorporation of human’s perception President University Erwin Sitompul NNFL 8/6

Fuzzy Logic Set Definition Classical Sets young = { x P | age(x) ≤ 20 } Characteristic function: 1 A=“young” 0 President University Erwin Sitompul NNFL 8/7

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] 1 A=“young” 1 0 President University A=“young” 0 Erwin Sitompul NNFL 8/8

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] 1 A=“young” 0 President University Erwin Sitompul NNFL 8/9

Fuzzy Logic Set Definition Some Definitions n Support of a fuzzy set A supp(A) = { x X | A(x) > 0 } n Core of a fuzzy set A core(A) = { x X | A(x) = 1 } n α-cut of a fuzzy set A Aα = { x X | A(x) α} (x) 1 α = 0. 6 0 President University Erwin Sitompul x NNFL 8/10

Fuzzy Logic Control (FLC) n 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. n FLC uses the IF-THEN rules, similar to binary control (Programmable Logic Controller, PLC). n Rule Format: n Ri: IF x is Aj AND y is Bk THEN z is Cl n Ri: IF x is Aj OR y is Bk THEN z is Cl President University Erwin Sitompul NNFL 8/11

Fuzzy Logic Operators President University Erwin Sitompul NNFL 8/12

Fuzzy Logic Operators Boolean OR and Fuzzy OR Boolean OR President University Fuzzy OR Erwin Sitompul NNFL 8/13

Fuzzy Logic Operators Boolean AND and Fuzzy AND Boolean AND President University Fuzzy AND Erwin Sitompul NNFL 8/14

Fuzzy Logic Control Example: Air Fan Control (Single Input) n Conventional (On-Off) Control: IF temperature > X °C, THEN run fan, ELSE stop fan. n 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. President University Erwin Sitompul NNFL 8/15

Fuzzy Logic Control Example: Heater Fan Control (Two Inputs) n Problem: Change the speed of the fan, based on the room temperature and humidity. n The temperature is classified into four conditions: Cold, Cool, Warm, and Hot. n The humidity can be defined by: Low, Medium, and High. n The available wattage settings of the heater fan are Zero, Low, Medium, and High. Temperature Humidity Fan Wattage President University Erwin Sitompul NNFL 8/16

Fuzzy Logic Control Example: Stopping A Car Break force Mass of the car Initial position Initial velocity President University Erwin Sitompul NNFL 8/17

Fuzzy Logic Control Example: Stopping A Car P-Control With Kp = – 240, the car will stop at the traffic light after 10 s. President University PD-Control Choosing ζ = 1, Td = 1, Kp = 6000, the car will stop at the traffic light after 5 s. Erwin Sitompul NNFL 8/18

Fuzzy Logic Control Example: Stopping A Car n Fuzzy Logic Control: n IF distance is long AND approach is fast, THEN brake zero; n IF distance is long AND approach is slow, THEN brake zero; n IF distance is short AND approach is fast, THEN brake hard; n IF distance is short AND approach is slow, THEN brake zero. President University Erwin Sitompul NNFL 8/19

Fuzzy Logic Control Example: Stopping A Car Fuzzy Membership Functions 100 m 25 m 0 m 100% ? ? 0% -100 m/s 100% -10 m/s ? ? 0 m/s 0% Negative to emphasize that the value is decreasing President University Erwin Sitompul NNFL 8/20

Fuzzy Logic Control Example: Stopping A Car Time Response President University Erwin Sitompul NNFL 8/21

Neural Networks Introduction Preparation Assignment n Ensure yourself to install Matlab in your computer, along with Matlab Simulink, Control System Toolbox, and Fuzzy Logic Toolbox. n The Fuzzy Logic Toolbox can be opened by typing “fuzzy” on the command window. n Read the Fuzzy Toolbox Manual that can be found in the directory where Matlab is installed. One version of the manual can be found on the lecture website. President University Erwin Sitompul NNFL 8/22

Neural Networks Introduction Homework 8 A n Conduct a literature research and prepare a short Power. Point presentation about the applications and implementations of fuzzy logics in: 1. Consumer electronics. (Fadhilla, Alief) 2. Defense and security. (Keanu, Maulidya) 3. Business decision making. (Andre, Fikri) 4. Psychology. (Rudy, Tamara) n Each group will be given 15 minutes time for presentation on Monday, 12. 03. 2018. President University Erwin Sitompul NNFL 8/23