![Fuzzy Logic Representation
Every problem must be
represent in terms of
fuzzy sets.
What are fuzzy sets?
Slowest
Fastest
Slow
Fast
[ 0.0 – 0.25 ]
[ 0.25 – 0.50 ]
[ 0.50 – 0.75 ]
[ 0.75 – 1.00 ]](https://image.slidesharecdn.com/fuzzyandnn-150510123133-lva1-app6892/85/Fuzzy-and-nn-6-320.jpg)
Fuzzy and nn
- 1. By Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh Fuzzy Logic and Artificial Neural Network using MATLAB
- 2. The term "fuzzy logic" was introduced with the 1965 proposal of fuzzy set theory by Lotfi A. Zadeh. Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 3. Fuzzy Controllers The Outputs of the Fuzzy Logic System Are the Command Variables of the Plant: Fuzzification Inference Defuzzification IFtemp=low ANDP=high THENA=med IF... Variables Measured Variables Plant Command
- 4. Conventional (Boolean) Set Theory: Fuzzy Set Theory “Strong Fever” 40.1°C 42°C 41.4°C 39.3°C 38.7°C 37.2°C 38°C Fuzzy Set Theory: 40.1°C 42°C 41.4°C 39.3°C 38.7°C 37.2°C 38°C “More-or-Less” Rather Than “Either-Or” ! “Strong Fever”
- 5. Traditional Representation of Logic Slow Fast Speed = 0 Speed = 1 bool speed; get the speed if ( speed == 0) { // speed is slow } else { // speed is fast } Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 6. Fuzzy Logic Representation Every problem must be represent in terms of fuzzy sets. What are fuzzy sets? Slowest Fastest Slow Fast [ 0.0 – 0.25 ] [ 0.25 – 0.50 ] [ 0.50 – 0.75 ] [ 0.75 – 1.00 ]
- 7. Fuzzy Logic Representation Slowest Fastest float speed; get the speed if ((speed >= 0.0)&&(speed < 0.25)) { // speed is slowest } else if ((speed >= 0.25)&&(speed < 0.5)) { // speed is slow } else if ((speed >= 0.5)&&(speed < 0.75)) { // speed is fast } else // speed >= 0.75 && speed < 1.0 { // speed is fastest } Slow Fast
- 9. 9 Fuzzy Linguistic Variables • Fuzzy Linguistic Variables are used to represent qualities spanning a particular spectrum • Temp: {Freezing, Cool, Warm, Hot} • Membership Function • Question: What is the temperature? • Answer: It is warm. • Question: How warm is it? Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 10. 10 Membership Functions • Temp: {Freezing, Cool, Warm, Hot} • Degree of Truth or "Membership" 50 70 90 1103010 Temp. (F°) Freezing Cool Warm Hot 0 1 Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 11. 11 Membership Functions • How cool is 36 F° ? 50 70 90 1103010 Temp. (F°) Freezing Cool Warm Hot 0 1 Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 12. 12 Membership Functions • How cool is 36 F° ? • It is 30% Cool and 70% Freezing 50 70 90 1103010 Temp. (F°) Freezing Cool Warm Hot 0 1 0.7 0.3 Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 13. 13 Fuzzy Logic • How do we use fuzzy membership functions in predicate logic? • Fuzzy logic Connectives: – Fuzzy Conjunction, – Fuzzy Disjunction, • Operate on degrees of membership in fuzzy sets Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 14. 14 Fuzzy Disjunction • AB max(A, B) • AB = C "Quality C is the disjunction of Quality A and B" 0 1 0.375 A 0 1 0.75 B (AB = C) (C = 0.75) Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 15. 15 Fuzzy Conjunction • AB min(A, B) • AB = C "Quality C is the conjunction of Quality A and B" 0 1 0.375 A 0 1 0.75 B (AB = C) (C = 0.375) Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 17. 17 Fuzzy Control • Fuzzy Control combines the use of fuzzy linguistic variables with fuzzy logic • Example: Speed Control • How fast am I going to drive today? • It depends on the weather. • Disjunction of Conjunctions Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 18. 18 Inputs: Temperature, Cloud Cover • Temp: {Freezing, Cool, Warm, Hot} • Cover: {Sunny, Partly, Overcast} 50 70 90 1103010 Temp. (F°) Freezing Cool Warm Hot 0 1 40 60 80 100200 Cloud Cover (%) OvercastPartly CloudySunny 0 1 Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 19. 19 Output: Speed • Speed: {Slow, Fast} 50 75 100250 Speed (mph) Slow Fast 0 1 Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 20. 20 Rules • If it's Sunny and Warm, drive Fast Sunny(Cover)Warm(Temp) Fast(Speed) • If it's Cloudy and Cool, drive Slow Cloudy(Cover)Cool(Temp) Slow(Speed) • Driving Speed is the combination of output of these rules... Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 21. 21 Example Speed Calculation • How fast will I go if it is – 65 F° – 25 % Cloud Cover ? Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 22. 22 Fuzzification: Calculate Input Membership Levels • 65 F° Cool = 0.4, Warm= 0.7 • 25% Cover Sunny = 0.8, Cloudy = 0.2 50 70 90 1103010 Temp. (F°) Freezing Cool Warm Hot 0 1 40 60 80 100200 Cloud Cover (%) OvercastPartly CloudySunny 0 1 Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 23. 23 ...Calculating... • If it's Sunny and Warm, drive Fast Sunny(Cover)Warm(Temp)Fast(Speed) 0.8 0.7 = 0.7 Fast = 0.7 • If it's Cloudy and Cool, drive Slow Cloudy(Cover)Cool(Temp)Slow(Speed) 0.2 0.4 = 0.2 Slow = 0.2 AB = min(A, B) Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 24. 24 Defuzzification: Constructing the Output • Speed is 20% Slow and 70% Fast • Find centroids: Location where membership is 100% 50 75 100250 Speed (mph) Slow Fast 0 1 Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 25. 25 Defuzzification: Constructing the Output • Speed is 20% Slow and 70% Fast • Speed = weighted mean = = (2*25+7*75)/(9) = 63.8 mph 50 75 100250 Speed (mph) Slow Fast 0 1 Mrs. Shimi S.L Assistant Professor,EE NITTTR, Chandigarh
- 27. ● Artificial neural network (ANN) is a machine learning approach that models human brain and consists of a number of artificial neurons. ● An Artificial Neural Network is specified by: − neuron model: the information processing unit of the NN, − an architecture: a set of neurons and links connecting neurons. Each link has a weight, − a learning algorithm: used for training the NN by modifying the weights in order to model a particular learning task correctly on the training examples. ● The aim is to obtain a NN that is trained and generalizes well. ● It should behaves correctly on new instances of the learning task.
- 28. The Biological Neural Network Characteristics of Human Brain • Ability to learn from experience • Ability to generalize the knowledge it possess • Ability to perform abstraction • To make errors.
- 29. • A neuron fires when the sum of its collective inputs reaches a threshold • There are about 10^11 neurons per person • Each neuron may be connected with up to 10^5 other neurons Consists of three sections cell body dendrites axon
- 30. • Nerve impulses which pass down the axon, jump from node to node, thus saving energy. • There are about 10^16 synapses. Usually no physical or electrical connection made at the synapse.
- 32. Human neurons Artificial neurons Neurons Neurons Axon, Synapse Wkj (weight) Synaptic terminals to next neuron output terminals Synaptic terminals taking input input terminals (Xj) human response time=1 ms silicon chip response time=1ns
- 33. Input values weights Summing function Bias b Activation functionInduced Field v Output y x1 x2 xm w2 wm w1 )( m 1 jjxwu j Perceptron: Neuron Model (Special form of single layer feed forward)
- 34. Neuron ● The neuron is the basic information processing unit of a NN. It consists of: 1 A set of links, describing the neuron inputs, with weights W1, W2, …, Wm 2 An adder function (linear combiner) for computing the weighted sum of the inputs: (real numbers) 3 Activation function for limiting the amplitude of the neuron output. Here ‘b’ denotes bias. m 1 jjxwu j )(uy b
- 35. Bias of a Neuron ● The bias b has the effect of applying a transformation to the weighted sum u v = u + b ● The bias is an external parameter of the neuron. It can be modeled by adding an extra input. ● v is called induced field of the neuron bw xwv j m j j 0 0
- 37. Activation Function ● The choice of activation function determines the neuron model. Examples: ● step function: ● ramp function: ● sigmoid function with z,x,y parameters ● Gaussian function: 2 2 1 exp 2 1 )( v v )exp(1 1 )( yxv zv otherwise))/())((( if if )( cdabcva dvb cva v cvb cva v if if )(
- 38. Training Training is accomplished by sequentially applying input vectors while adjusting network weights according to a predetermined procedures. Supervised Training requires the pairing of each input vector with a target vector representing the desired output. Unsupervised Training requires no target vector for the output and no comparisons to predetermined ideal responses. The training algorithm modifies network weights to produce output vectors that are consistent. Also called self- organizing networks.
- 39. Gradient descent or Steepest Descent ɳ is the learning rate global minimum
- 40. X1 1 true true false true 0 1 X2 Boolean function OR – Linearly separable
- 41. These two classes (true and false) cannot be separated using a line. Hence XOR is non linearly separable. Input Output X1 X2 X1 XOR X2 0 0 0 0 1 1 1 0 1 1 1 0 X1 1 true false false true 0 1 X2
- 42. Multi layer feed-forward NN (FFNN) ● FFNN is a more general network architecture, where there are hidden layers between input and output layers. ● Hidden nodes do not directly receive inputs nor send outputs to the external environment. ● FFNNs overcome the limitation of single-layer NN. ● They can handle non-linearly separable learning tasks. Input layer Output layer Hidden Layer 3-4-2 Network
- 43. FFNN for XOR ● The ANN for XOR has two hidden nodes that realizes this non-linear separation and uses the sign (step) activation function. ● Arrows from input nodes to two hidden nodes indicate the directions of the weight vectors (1,-1) and (-1,1). ● The output node is used to combine the outputs of the two hidden nodes. Input nodes Hidden layer Output layer Output H1 –0.5 X1 1 –1 1 Y –1 H2 X2 1 1
- 44. Inputs OutputofHiddenNodes Output Node X1XORX2 X1 X2 H1 H2 0 0 0 0 –0.50 0 0 1 –10 1 0.5 1 1 1 0 1 –10 0.5 1 1 1 1 0 0 –0.50 0 Since we are representing two states by 0 (false) and 1 (true), we will map negative outputs (–1, –0.5) of hidden and output layers to 0 and positive output (0.5) to 1. Input nodes Hidden layer Output layer Output H1 –0.5 X1 1 –1 1 Y –1 H2 X2 1 1
- 45. Hardware Implementation • Dspace • Quad-Core AMD Opteron processor
- 47. Opal RT
- 48. 48 Thank you. Questions, Comments, …? Shimi.reji@gmail.com 9417588987
- 49. • Human can identify a person through thoughts.which means humans neurons are getting trained itself. Therefore through Artificial Neural Network we can train artificial neurons using computer programming . using neural network we are trying to build a network between neurons to transfer the electrical signals.which are consists of neural commands . • usually Computer response time is 10^6 times faster than humans response time because of the silicon Integrated chips. • silicon chip response time :- 1 nanosecond • human response time :- 1 millisecond • • but human can perform faster than chips because human has massively parallel neural structure. If we consider human neuron structure it has synaptic terminals, cell body(neurons), basal dendrite and axon. Each components has some function to transfer signal to neurons.
- 50. • Bias neurons are added to neural networks to help them learn patterns. A bias neuron is nothing more than a neuron that has a constant output of one. Because the bias neurons have a constant output of one they are not connected to the previous layer. The value of one, which is called the bias activation, can be set to values other than one. However, one is the most common bias activation.