The document discusses design aspects of fuzzy logic systems, including an introduction to fuzzy sets and classical sets. It defines universal sets, fuzzy sets, and membership functions. Various types of membership functions are described, including triangular, trapezoidal, Gaussian, bell-shaped, and sigmoid functions. Membership functions generalize indicator functions for classical sets by representing degrees of truth.

1. Design Aspects of Fuzzy Logic Systems
1

2. Introduction to fuzzy sets
Classical set/Crisp Set
Properties of classical set/Crisp set
Fuzzy set
Representation of fuzzy set
2

3. Classical set/Crisp set (A)
• Universal set (X) : A set consist of all possible elements
Ex: All technical Universities in the world
• It is a set with well defined boundary
Ex: A set of technical universities having at least 5 departments each
3

4. 4

5. 5

6. 6

7. 7

8. 8

9. 9

10. Convex Vs Non-Convex Membership function
10
The Membership Function of a fuzzy set is a generalization of the indicator
function for classical sets. In fuzzy logic, it represents the degree of truth as an
extension of valuation.

11. Various types of membership function distribution
11
• 1. Triangular Membership function
• 2. Trapezoidal Membership function
• 3. Gaussian Membership function
• 4. Bell shaped Membership function
• 5. Sigmoid Membership function

12. 12

13. Thank You
13