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Prepared by:
Bhaumikkumar P Parmar
Department of Computer Engineering
Government Engineering College, Modasa
Outline
 Fuzzy Logic
 Fuzzy Set
 Fuzzy Set & Classical Set
 Membership Function
 Fuzzy Set Operations
 Fuzzy Logic S...
Fuzzy Logic
 We talk about real world , our expression about real world , the
way we describe real world are not very pre...
Fuzzy Logic
• Since we use imprecise data in our communication language,
then it must be associated with some logic.
• The...
Fuzzy set
• Classical Set : A={a1,a2,a3,a4…,an}
• Set A can be represented by Characteristic function.
μa(x)={ 1 if elemen...
Fuzzy set & Classical set
• Consider universal set T which stands for tempratute.
• Cold , Normal , Hot are the subset of ...
Fuzzy set & Classical set
• In Contrast Fuzzy Set have soft boundary .
• cold normal hot
• 𝜇𝑥 1
•
• 0.5
• 5 10 15 20 25 30...
Membership Function
• A member function is a function that defines degree of an
element’s membership in fuzzy set.
adult(x...
Membership Function
There are different form of membership function.
Linguistic Variable
 Linguistic variables are the input or output variables of the
system whose values are words or sente...
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
...
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
...
Fuzzy Set & Probabilities
• The values attached to properties in fuzzy logic are in some
ways like probabilities, but it i...
Fuzzy Logic System
Fuzzy Logic System
• The rule base and database are jointly referred to as
knowledge base.
• A rule base containing a numb...
Example
To estimate the level of risk in project.
 For the sake of simplicity we will arrive at our conclusion
based on t...
Example
1)Define linguistic variables and terms.
For Input:-
For Project funding : inadequate, marginal , adequate
For Pro...
Example
2)Construct membership function.
Input output
Example
3)Construct the rule base .
 If project funding is adequate or project staffing is small
then risk is low.
 If p...
Example
4)Convert crisp input data to fuzzy values.(fuzzification)
Project funding=26% .
Inadequate =0.4
marginal=0.2
adeq...
Example
5)Evaluate the rule in rule base (inference)
 If project funding is adequate or project staffing is small then ri...
Example
5)Evaluate the rule in rule base (inference) (continue)
 If project funding is inadequate then risk is high.
inad...
Example
6)Convert the output data to non-fuzzy values(defuzzification).
centroid method :
cog=(((0+10+20)*0.2)+((30+40+50+...
Example
Advantage
 Mathematical concepts within fuzzy reasoning are very
simple.
 You can modify a FLS by just adding or deletin...
Disadvantage
 There is no systematic approach to fuzzy system designing.
 They are understandable only when simple.
 Th...
Fuzzy Application
• Many of the early successful applications of fuzzy logic were
implemented in Japan.
• The first notabl...
Bibliography
BOOK :
Artificial Intelligence by Elaine Rich, Kelvin Knight and
Shivashankar B Nair.
WEBSITES :
•http://www....
Thank You
Fuzzy Logic Seminar with Implementation
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Fuzzy Logic Seminar with Implementation

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fuzzy logic system implemented in scilab. fuzzy logic seminar presentation

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  • you can design your fuzzy logic.it was one example taken from book.you can provide user to input his choice in fuzzy terms.
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Fuzzy Logic Seminar with Implementation

  1. 1. Prepared by: Bhaumikkumar P Parmar Department of Computer Engineering Government Engineering College, Modasa
  2. 2. Outline  Fuzzy Logic  Fuzzy Set  Fuzzy Set & Classical Set  Membership Function  Fuzzy Set Operations  Fuzzy Logic System  Example  Advantage  disadvantages  Application
  3. 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. 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. 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. 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. 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. 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. 9. Membership Function There are different form of membership function.
  10. 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. 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. 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. 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. 14. Fuzzy Logic System
  15. 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. 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. 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. 18. Example 2)Construct membership function. Input output
  19. 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. 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. 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. 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
  23. 23. 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%
  24. 24. Example
  25. 25. 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.
  26. 26. 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.
  27. 27. 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.
  28. 28. 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
  29. 29. Thank You

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