Gives introduction about Fuzzy Sets and Membership Function, Fuzzy Operation

1. Fuzzy Set
Soft Computing

2. Fuzzy Set
01
Set Theoretic Operation
02
MF Formulation
03
Agenda

3. Fuzzy Set-
Intro

4. Introduction
.
In contrast to Classical Set , Fuzzy set does not have crisp boundary.
It is Characterized by Membership functions that gives flexibility that
uses linguistic expression.
Fuzziness comes from uncertain and imprecise nature of abstract
thoughts and concepts.
Membership function assigns each object a grade of membership ranging
between 0 to 1.
Grade of membership depends on the context in which it is considered.
The notion of inclusion, union, intersection, complement and relation can
be extended

5. Introduction
.
In real world, Human thinking and reasoning represents fuzzy
information.
Developed system will not be able to answer to many questions when it
is a classical set.
We are in need to develop a system that should be built with incomplete
and unreliable information.
So we need to describe a set with unambiguous boundary, there is a
uncertainty in set boundary.
Thus fuzzy logic is able to handle imprecise concepts.

6. Fuzzy Sets
.
 If X is an universe of discourse and x is a particular element of X,
then a fuzzy set A defined on X and can be written as a collection of
ordered pairs
A = {(x, µÃ (x)), x є X }
Let for example X be the Tall Person with the membership Tall takes
value between [0,1]
Here Tall is the Fuzzy Term with µ as its membership function

7. Membership function
.
 It measures the degree of similarity of an element to a fuzzy set.
It can be chosen by user arbitrarily based on user experience.
Or it can be chosen by machine learning models
The membership function can be
Triangular
Trapezoidal
Gaussian

8. Triangular Member function
.
Three parameters are required to specify the membership function
values.
{ a, b, c} where a is the lower boundary, c is upper boundary with
value 0 and b is the center with the highest value 1.

9. Trapezoidal Member function
.
It takes 4 parameters {a, b, c, d}

10. Features of Member function
.
Boundary, Support and Core are the features

11. Gaussian Member function
.
It takes 3 parameters { c, s, m} c be the center, s be the width and m is
the fuzzification factor

12. Fuzzy Set Operations
.
The operations are union, intersection, complement,

13. THANK YOU