dempster combinations theory

1. Dempster Shafer Theory
By
Md. Fazle Rabbi
16CSE057

2. 4.2
Contents
⮚ Definition
⮚ Why DS theory
⮚ Example
⮚ Characteristic
⮚ Advantage

3. 4.3
Definition
The theory of belief functions, also referred to as
evidence theory or Dempster–Shafer theory, is a general
framework for reasoning with uncertainty, with
understood connections to other frameworks such as
probability, possibility and imprecise probability theories.

4. 4.4
Why DS Theory?
• Bayesian Theory is only concerned about single
evidence.
• Bayesian Theory can not describe ignorance.

5. 4.5
Example

6. 4.6
Let us comsider a room where 4 persons are
presented
Figure 1 Example

7. 4.7
Figure 2 Example

8. 4.8
Figure 2 Example
Who is the murderer ?

9. 4.9
To Solve this, let us consider some following
possibilities
• Either {A} or {C} or {D} have killed him.
• Either {A,C} or {C,D} or {A,D} have killed him.
• Or the three of them have killed him i.e:{A,C,D}
• None of them killed him.
Using the above example we can say:
Set of possible conclusion (P)=(P1,P2….Pn)
Power set will contain 2n elements where n is number of
elements of the possible set.
If P={a,b,c}, then power set is given as
{0,{a},{b},{c},{a,b},{a,c},{b,c},{a,b,c} = 2^3 elements.

10. 4.10
The Characteristic in this model
● Ignorance is reduced in this theory by adding
more and more evidences.
● Combination rule is used to combine various
types of possibilities.

11. 4.11
Advantage
● As we add more information uncertainty interval
reduces.
● DST has much lower level of ignorance
● Diagnose hierarchies can be represented using
this
● Person dealing with such problems is free to
think about evidences.

12. 4.12
Thank You