Generate the population in the next iteration by using Roulette-Wheel criterion:
|
|
|
| 1 | 3.5 |
| 2 | 4.6 |
| 3 | 5 |
| 4 | 2.8 |
| 5 | 1.8 |
First, compute the total fitness of the population: [ F_\text{total} = 3.5 + 4.6 + 5 + 2.8 + 1.8 ] Step by step: * (3.5 + 4.6 = 8.1) * (8.1 + 5 = 13.1) * (13.1 + 2.8 = 15.9) * (15.9 + 1.8 = 17.7) So, (F_\text{total} = 17.7). Next, compute the selection probability (p_k) for each individual: [ p_k = ____ ________ _______ ____ ___ ___ ____.
_________ ____ _________ ________ ___ ____.
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_____ __________ ________ ___ _____ ____ ______ _______ ______ _________ _________ ____.
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___ _____ _____ __________ _________ ___ __________ _______ ________.
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__________ __________ _____ ________ __________ __________ _________ _____.
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_____ ________ _______ ________ ________ __________ ________ _________.
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___ ____ ____ _____ _____.
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(क) के एक विवृत उपसमुच्चय D पर दो अवकलनीय फलनों f और g की फलनात्मक आश्रितता का आवश्यक प्रतिबंध बताने वाले प्रमेय का कथन दीजिए। निम्नलिखित फलनों f तथा g द्वारा परिभाषित इस प्रमेय को सत्यापित कीजिए।
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(ख) अस्पष्ट फलन प्रमेय की सहायता से यह दिखाइए कि 1 के प्रतिवेश में एक ऐसा अवकलनीय फलन g होता है, जिससे कि (2,1) के प्रतिवेश में और
जहाँ
से फलन F परिभाषित है। g'(y) भी ज्ञात कीजिए।
(ग) द्वारा परिभाषित फलन f की (1, -1) पर स्थानीय व्युत्क्रमणीयता की जाँच कीजिए। फलन f के लिए एक प्रांत ज्ञात कीजिए जिसमें f व्युत्क्रमणीय है।
Consider the following table for the connections between input neurons and the hidden layer neurons:
| Input Neurons | Hidden Layer Neurons | Connection Weight |
| 1 | 1 | - 1 |
| 1 | 2 | - 0.1 |
| 1 | 3 | 1 |
| 2 | 1 | - 1 |
| 2 | 2 | 1 |
| 2 | 3 | 1 |
| 3 | 1 | - 0.2 |
| 3 | 2 | - 0.3 |
| 3 | 3 | - 0.6 |
Determine the fuzzy relation T as a composition between the fuzzy relations R and S given below by using max-min and max-product:
Using diagram, show the difference between feed-forward neural network and recurrent neural network.
State whether the following statements are True or False. Give short proof or a counter example in support of your answer.
a) In the Hopfield network, the neurons belonging to the same layer receive input from the neurons of the previous layer and send their value only to the neurons of the next layer.
b) The length of chromosomes to determine the maximum value of the set:
is 12.
c) The fuzzy relation (R) given below, is an equivalence relation.
d) The Self Organizing Map (SOM) is a supervised learning technique.
e) In a single layer neural network, if , then the output is -1.
Solve the network to approximate the function:
for , choosing the initial weights and bias as the random numbers.
Computer the output for the neurons in the kohonen networks, the related data is given below:
i) Input to Kohnen neural network:
Input Neuron-1
Input Neuron-2
ii) Connected weights between the neurons are as given below: