Soft-Computing-and-Fuzzy-Logic

Topics Covered in the Assignments

A. Fuzzy Logic

1. Fuzzy Set Operations

2. Membership functions

3. Fuzzy Rules

4. Fuzzy Inference System

B.Genetic Algorithms

A. Fuzzy Logic

Assignment 1

On two fuzzy sets A and B, Implement the following Fuzzy Set Operations:

1. Sum (A+B)
2. Difference (A-B)
3. Cartesian product
4. Union (AUB)
5. Intersection of A and B
6. Complement of A

Assignment 2

Implement the following membership functions:

1. Triangular
2. Trapezoidal
3. Gaussian
4. Generalized Bell
5. Sigmoidal

Assignment 3

Find applications where you find fuzzy logic to be suitable

Assignment 4

Find specific scenarios where Gaussian Membership function can be applied

Assignment 5

Implement min-max and max-product composition 4

Assignment 6

Consider a universe representing room temperature in degree C and other universe representing relative humidity given by

T = 0.4/16 +0.8/18+1.0/20+1.0/22+0.8/24+0.5/26

H= 0.2/0+0.8/20+1.0/40+0.6/60+0.2/80

Calculate the membership of “ Acceptable Temperature OR Acceptable Humidity”.

Assignment 7

Given, following membership functions for fuzzy sets old and young ( ) ( ) ( ) ( ) Where, x is the age of the person. Calculate the value of the following:

1. More or less young
2. Not young and not old
3. Young but not too young
4. Extremely old

Assignment 8

Given, following relations: R1 = “x is relevant to y” R2 = “y is relevant to z” 5 Where X= {1, 2, 3} Y= {a,b,c,d} Z = {one, two} Assuming appropriate values for R1 and R2, calculate the max-min composition and max product composition for (3, one).

Assignment 9

Take different elements of a fuzzy set as user input and defuzzify using Bisector of area, Centroid of area, Mean of Maximum and Smallest of maximum.

Assignment 10

Given, following rules: Rule 1: If BP is high and temperature is high then health is Poor Rule2: If BP is normal and temperature is normal then health is Good Rule 3: If BP is low and temperature is normal then health is Normal. Take the values of Blood Pressure and Temperature as User input and determine the health of the person. 6

Assignment 11

Solve the Air conditioner controller problem using Fuzzy Inference System. Frame the rules. Compare the results using Mamdani, Sugeno and Tsukamoto FIS. An example of Fuzzy Rule Base could be something like this Rules Temperature Humidity Compressor speed

1. Very Low Dry Off
2. Very Low Comfortable Off
3. Very Low Humid Off
4. Very Low Sticky Low
5. Low Dry Off
6. Low Comfortable Off
7. Low Humid Low
8. Low Sticky Medium
9. High Dry Low
10. High Comfortable Medium
11. High Humid Fast
12. High Sticky Fast
13. Very High Dry Medium
14. Very High Comfortable Fast
15. Very High Humid Fast
16. Very High Sticky Fast

Assignment 12

Design a Fuzzy logic based washing control on a Washing machine The amount of water, dirt in the cloth and other parameters will decide the time taken in washing Initialize input parameters like washing time, amount of dirt etc. -> Initialize fuzzy system with membership function-> Define fuzzy rules->Get fuzzy decision for washing time prediction 7

B. Genetic Algorithms

Assignment 13

For any sample data set, implement Order Encoding for Travelling Salesman Problem

Assignment 14

For any sample data set, implement Binary Encoding for 0/1 Knapsack problem

Assignment 15

Use proper encoding technique to represent a chromosome in 8- queens problem.

Assignment 16

Given, a population of size N, create a mating pool of Np individuals using different selection techniques that you have studied in your lectures.

Assignment 17

Use GA to solve the following nonlinear programming problem Minimize ( ) ( )

Subject to

X1 and x2 have three and two decimal places respectively 8

1. Encode using binary encoding
2. Compute the fitness and perform crossover and mutation to yield optimum results.