![Systems are Fuzzy
• We need to be able to create systems that
can cope with fuzzy data
• Fuzzy logic is logic that is used to describe
fuzziness and uses fuzzy sets
1
0
0 75 Age
A Linear membership function
shows the gradual transition
of membership
(x)young
The membership function, A defines the fuzzy set, A
A : X [0,1]](https://image.slidesharecdn.com/introduction-fllofti-240410054432-92706e49/85/Introductionfuzzy-7-320.jpg)
Introductionfuzzy...................................
- 1. The World is a Fuzzy Place A Beginners Guide To Fuzzy Logic Brought to you by the IEEE Computational Intelligence Society Pre-College Subcommittee
- 2. Tutorial Summary • Engineering the world……. • The world is not just BLACK and WHITE. • What does it really mean to be tall ? • Fuzzy sets and how you create them. • So you think you can boil a perfect egg ?
- 3. How Engineers Make a World of Difference You can change the World !
- 6. Human Dialog is Fuzzy • Experts rely on common sense when they solve problems. • How can we represent expert knowledge that uses vague and ambiguous terms in a computer? • Does a computer understand the difference between a young person and an old person ? • If we store age as a numeric value then this is quite precise e.g. age is between 0 and 115 • However if in our data, age has values like old, medium, and young then this is fuzzy.
- 7. Systems are Fuzzy • We need to be able to create systems that can cope with fuzzy data • Fuzzy logic is logic that is used to describe fuzziness and uses fuzzy sets 1 0 0 75 Age A Linear membership function shows the gradual transition of membership (x)young The membership function, A defines the fuzzy set, A A : X [0,1]
- 8. Professor Lofti Zadeh • In 1965 Lotfi Zadeh, published his famous paper “Fuzzy sets”. • Meet Professor Lofti Zadeh in a short interview when he was awarded the Benjamin Franklin Medal of Electrical Engineering.
- 9. What is Short and Tall ? height 0 1 short tall 200 cm 0 cm 165 cm My younger brother is quite short This is a tall tree !
- 10. Activity: Creating Fuzzy Sets • All stand up and make a line from smallest to tallest in terms of height – Record the height of everyone in your class – Who is the tallest and the shortest? – Assuming you have three labels “Tall”, “Medium” and “Short” assign each person in the class a label ? • How did you decided on who goes where ? i.e. determined the boundaries ? • Could you agree ?
- 11. Example of Pupils Name Height (cm) SHORT MEDIUM TALL Jane 180 √ Alex 177 √ Haider 175 √ Surni 165 √ √ Max 142 √ Jo-ellen 142 √ Kaprisa 140 √ Stephen 139 √ Jo 100 √ √ Pei 98 √ So who is Short ? Medium ? Tall ?
- 12. Drawing Crisp Sets • First draw some crisp sets 0 1 short tall 0 cm 165 cm medium 200 cm 100 cm height Grade Of Membership
- 13. How much do pupils belong in the fuzzy sets ? • We need to know the degree in which each person belongs to the fuzzy sets short, medium and tall. • Assume we decide short is any heights between 0 and 100 cm then the fuzzy set short is defined as: 100 0 100 0 100 1 0 1 ) , 100 , 0 ( height height height height height Short
- 14. How much do pupils belong in the fuzzy sets ? • Assume we decide tall is any heights greater that 165cm then the fuzzy set tall is defined as: 200 1 200 165 35 165 165 0 ) , 100 , 0 ( height height height height height Tall This example shows that anyone over 200cm is always definitely Tall !
- 15. So what about Medium ? • A medium height person may be someone between 80 cm and 185 cm so we need to create a triangular fuzzy set to cover this range. 185 0 185 133 52 185 133 80 53 80 80 0 ) ( height if height if height height if height height if height Medium Note: 133cm is the midpoint of the triangular fuzzy set !
- 16. Pupils Membership Name Height (cm) SHORT MEDIUM TALL Jane 180 0 0 0.43 Alex 177 0 0 0.34 Haider 175 0 0 0.29 Surni 165 0 0.39 0 Max 142 0 0.83 0 Jo-ellen 142 0 0.83 0 Kaprisa 140 0 0.87 0 Stephen 139 0 0.89 0 Jo 100 0 0.38 0 Pei 98 0.02 0 0
- 17. Drawing Fuzzy Sets • Now draw your fuzzy sets 0 1 short tall 0 165 185 medium 200 80 100 Height in CM 133 Grade Of Membership
- 18. Everyday Fuzzy Words Can you identify other fuzzy keywords that you use everyday ?
- 20. So you think you can boil a perfect egg ? The Perfect Egg = Soft Boiled.
- 21. Activity: Boiling an Egg • Discussion – How to come up with membership functions, based on our experience. • How small is a small egg? How large is a large egg? • What is soft ? What is hard ? – The process of fuzzification will define our fuzzy sets – The process of fuzzification • how long do we actually need to boil the egg ?
- 23. Experiment: Boiling an Egg Soft-Boiled Eggs 44 grams 50 grams 63 grams 4 minutes 5 minutes 6 minutes 7 minutes • Boil some eggs • Make sure you weigh them first !! • Fill in the table (or similar on Activity Sheet 2)
- 24. Multiple IF/THEN rules • A common misconception is that Fuzzy Logic is an IF/THEN/ELSE statement. • e.g. if small volume of water in kettle, heat it for 1 minute to boil; if large volume of water in kettle, heat for 3 minutes to boil. • So how long should you boil a kettle if it is half full ? • Discuss !
- 25. So you want to know more ? • Watch an Introduction to Fuzzy Logic.. • How is your life fuzzy ?