fuzzy logic system implemented in scilab. fuzzy logic seminar presentation

1. Prepared by:
Bhaumikkumar P Parmar
Department of Computer Engineering
Government Engineering College, Modasa

2. Outline
 Fuzzy Logic
 Fuzzy Set
 Fuzzy Set & Classical Set
 Membership Function
 Fuzzy Set Operations
 Fuzzy Logic System
 Example
 Advantage
 disadvantages
 Application

3. Fuzzy Logic
 We talk about real world , our expression about real world , the
way we describe real world are not very precise.
 Ex. Height (short, medium, tall), temperature(very hot, hot,
cold).
 Fuzzy logic is logic which is not very precise.
 Normally in real world we deal with this imprecise way .
 Computation that involves logic of impreciseness is much more
powerful than computation that is being carried through a
precise manner.

4. Fuzzy Logic
• Since we use imprecise data in our communication language,
then it must be associated with some logic.
• The father of fuzzy logic is Lotfi Zadeh from U C Berkeley in
1965, he pioneered research in fuzzy logic.
• The logic which can manipulate imprecise data is Fuzzy Logic.
• Fuzzy Logic has been applied to many fields , from control
theory to artificial intelligence.

5. Fuzzy set
• Classical Set : A={a1,a2,a3,a4…,an}
• Set A can be represented by Characteristic function.
μa(x)={ 1 if element x belongs to the set A
0 otherwise }
• Ex. A={ 1,2,3,4,5,6,7,8,9,10}.
• Fuzzy Set: A={{ x, μa(x) }}
where, μa(x) is the membership grade of a element x in fuzzyset
μa(x)=[0,1]
• Ex. Set of all tall people.
A={{5.9,0.4},{6.0,0.7},{6.1,0.9}}

6. Fuzzy set & Classical set
• Consider universal set T which stands for tempratute.
• Cold , Normal , Hot are the subset of universal set T.
• Classical Set (Crisp set)
• Cold={ temp ∈ T : 5° C < temp < 15° C }
• Normal={temp ∈ T : 15° C < temp < 25° C }
• Hot={temp ∈ T : 25° 𝐶 < 𝑡𝑒𝑚𝑝 < 35° 𝐶 }
• 14.9 ° C is Cold while 15.1 ° C is Normal .
• This shows that classical set have very rigid boundries.

7. Fuzzy set & Classical set
• In Contrast Fuzzy Set have soft boundary .
• cold normal hot
• 𝜇𝑥 1
•
• 0.5
• 5 10 15 20 25 30 35 40
• temp (°𝐶)
• The temprature 15° C is a member of two fuzzy sets , cold and
normal with a membership grade
• 𝜇𝑥(Cold)= 𝜇𝑥(Normal) = 0.5

8. Membership Function
• A member function is a function that defines degree of an
element’s membership in fuzzy set.
adult(x)= { 0, if age(x) < 16years
(age(x)-16years)/4, if 16years < = age(x)< = 20years,
1, if age(x) > 20years }

9. Membership Function
There are different form of membership function.

10. Linguistic Variable
 Linguistic variables are the input or output variables of the
system whose values are words or sentences from a natural
language, instead of numerical values. A linguistic variable
is generally decomposed into a set of linguistic terms.
 Ex . For air conditioner , temperature is linguistic variable.
 Temperature can quantify into too-cold, cold, warm, hot.
 They are the linguistic terms.
 They cover a portion of overall values of Temperature

11. Fuzzy Set Operations
• Let us consider two fuzzy sets
• A={
0
1
,
1
2
,
0.5
3
,
0.3
4
,
0.2
5
} and B={
0
1
,
0.5
2
,
0.7
3
,
0.2
4
,
0.4
5
}
• We can evaluate different fuzzy operation.
• Union: A∪ 𝐵 = max{ μ𝐴 𝑥 , μ𝐵 𝑥 }
= {
0
1
,
1
2
,
0.7
3
,
0.3
4
,
0.4
5
}
• Intersection: A∩ 𝐵 = m𝑖𝑛{ μ𝐴 𝑥 , μ𝐵 𝑥 }
= {
0
1
,
0.5
2
,
0.5
3
,
0.2
4
,
0.2
5
}

12. Fuzzy Set Operations
• Let us consider two fuzzy sets
• A={
0
1
,
1
2
,
0.5
3
,
0.3
4
,
0.2
5
} and B={
0
1
,
0.5
2
,
0.7
3
,
0.2
4
,
0.4
5
}
• We can evaluate different fuzzy operation.
• Complement: ¬𝐴 = 1 − μ𝐴 𝑥 = {
1
1
,
0
2
,
0.5
3
,
0.7
4
,
0.8
5
}
• Difference : A|B = 𝐴 ∩ ¬𝐵
= {
0
1
,
1
2
,
0.5
3
,
0.3
4
,
0.2
5
} ∩ {
1
1
,
0.5
2
,
0.3
3
,
0.8
4
,
0.6
5
}
= {
0
1
,
0.5
2
,
0.3
3
,
0.3
4
,
0.2
5
}

13. Fuzzy Set & Probabilities
• The values attached to properties in fuzzy logic are in some
ways like probabilities, but it is clearly not probabilities that
we are dealing with here.
• We may know Jack's height exactly. The assertion ‘Jack is
tall (0.75)’ measures how well Jack’s height matches the
sense of the word ‘tall’.
• On the other hand, ‘the probability that Jack is tall is 0.75’
would normally be used in a situation where we don't
actually know Jack's height.

14. Fuzzy Logic System

15. Fuzzy Logic System
• The rule base and database are jointly referred to as
knowledge base.
• A rule base containing a number of fuzzy IF-THEN rules;
• A database which defines the membership functions of
fuzzy sets used in fuzzy rules.
• fuzzification: converts crisp input to a linguistic variable
using membership function stored in fuzzy knowledge
base.
• Inference engine: using If-Then type fuzzy rules converts
the fuzzy input to fuzzy out
• Defuzzification: Converts the fuzzy output of the inference
engine to crisp using membership functions analogous to
the ones used by the fuzzifier.

16. Example
To estimate the level of risk in project.
 For the sake of simplicity we will arrive at our conclusion
based on two inputs: project funding and project staffing.
 Suppose our our inputs are project_funding =
26% and project_staffing = 54%.
 Find risk percentage.

17. Example
1)Define linguistic variables and terms.
For Input:-
For Project funding : inadequate, marginal , adequate
For Project staffing : small , large
For Output:-
For Project risk :low , normal , high.

18. Example
2)Construct membership function.
Input output

19. Example
3)Construct the rule base .
 If project funding is adequate or project staffing is small
then risk is low.
 If project funding is marginal and project staffing is large
then risk is normal.
 If project funding is inadequate then risk is high.

20. Example
4)Convert crisp input data to fuzzy values.(fuzzification)
Project funding=26% .
Inadequate =0.4
marginal=0.2
adequate=0.0
Project staffing=54%
small=0.2
Large=0.7

21. Example
5)Evaluate the rule in rule base (inference)
 If project funding is adequate or project staffing is small then risk
is low.
adequate(Project funding) ∨ small(Project staffing) ⇒ low(risk)
0.0 ∨ 0.2 ⇒ 0.2 low = 0.2
 If project funding is marginal and project staffing is large then
risk is normal.
marginal(Project funding) ∧ large(Project staffing) ⇒ normal(risk)
0.2 ∧ 0.7 ⇒ 0.2 normal = 0.2

22. Example
5)Evaluate the rule in rule base (inference) (continue)
 If project funding is inadequate then risk is high.
inadequate(Project funding) = high(risk)
inadequate(Project funding)=0.4
high =0.4
• so for risk : low =0.2 , normal =0.2 , high=0.4

24. Example
6)Convert the output data to non-fuzzy values(defuzzification).
centroid method :
cog=(((0+10+20)*0.2)+((30+40+50+60)*0.2)+((70+80+90+100)*0.4))
((3*0.2)+(4*0.2)+(4*0.4))
cog=58.666667%
Risk=58.67%

25. Example

26. Advantage
 Mathematical concepts within fuzzy reasoning are very
simple.
 You can modify a FLS by just adding or deleting rules due to
flexibility of fuzzy logic.
 Fuzzy logic Systems can take imprecise, distorted, noisy
input information.
 FLSs are easy to construct and understand.
 Fuzzy logic is a solution to complex problems in all fields of
life, including medicine, as it resembles human reasoning
and decision making.

27. Disadvantage
 There is no systematic approach to fuzzy system designing.
 They are understandable only when simple.
 They are suitable for the problems which do not need high
accuracy.
 Requires tuning of membership functions.

28. Fuzzy Application
• Many of the early successful applications of fuzzy logic were
implemented in Japan.
• The first notable application was on the high-speed train
in Sendai, in which fuzzy logic was able to improve the
economy, comfort, and precision of the ride.
• recognition of hand written symbols in Sony pocket
computers,
• flight aid for helicopters,
• In vehicle used as antilock brake system .
• single-button control for washing machines,
• As temperature controllers in Air conditioners,
Refrigerators.

29. Bibliography
BOOK :
Artificial Intelligence by Elaine Rich, Kelvin Knight and
Shivashankar B Nair.
WEBSITES :
•http://www.seattlerobotics.org/encoder/mar98/fuz/flindex.html
https://www.tutorialspoint.com/artificial_intelligence/artificial_int
elligence_fuzzy_logic_systems.htm
• http://en.wikipedia.org/wiki/Fuzzy_logic
• http://www.dementia.org/~julied/logic/index.html
• http://mathematica.ludibunda.ch/fuzzy-logic.html

30. Thank You