Principles of Information Science
Chapter 7
Information Regeneration
-- Decision Making Theory
List of Contents
1,From Knowledge to Strategy
2,Classical Model of Decision-Making
3,Information Theory of Decision-Making
4,Unified Theory
From Knowledge to Strategy
1,
Model of Information Regeneration
Information
Regeneration Knowledge
about the
Problem and
Environment
Strategy Information
for solving problem
under the given
environment
Goal to be sought
Knowledge and Strategy
Knowledge,A set of descriptions about the states
and the varying laws of the states
of certain categories of objects,
Strategy,A sequence of well organized action orders
for solving specific problems under certain
environment and certain goal,
Strategy can also be regarded as a special group of
information indicating the specific procedure of
problem solving,
Mechanism, from Knowledge to Strategy
P
Initial State
of Database Operation
New
State
Goal
Match
G
Rule
Base
Knowledge
Base
Rule
Sequence
N
Y
Strategy
Distance
Indication Control
E
Algorithm for Knowledge Activation
1,Given P(the Initial State of the Problem),E(the Knowledge
and the Rule Bases) and G(the Final State of the Problem)
2,Select the best Rule,from the Rule Base,so that whose left
side matches the Initial State while whose right side leads to
such a New State whose distance to the Goal is the minimum
compared with other selections by using the Knowledge
3,Check the New State thus obtained,If its distance to the
Goal is the smallest one but unequal to zero,do the same
thing from the New State as did in step 2
4,Otherwise,re-select a rule at step 2
5,Until the distance between the New State and the Goal
equal to zero,or sufficiently small,go loop from step 2 to 4,
The sequence of the rule applications is the strategy sought,
Classical Model of Decision-Making
2,
An Example,Umbrella Tricky
Benefits Table
Weather
Benefits
actions
Sunny Raining
Carry
a(1)
Not Carry
a(2)
p 1-p
c(1,1) c(1,2)
c(2,1) c(2,2)
Decision Rule
C(1) = p c(1,1) + (1-p) c(1,2)
C(2) = p c(2,1) + (1-p) c(2,2)
Calculate the average benefit for each action,
Choose the action with bigger benefit as the strategy,
If C(1) > C(2) then a(1) is chosen;
Otherwise,a(2) is chosen,
Model of Decision-Making
A(X) C
I(X;R)
DM
R
A(G)
G X
Information Theory of Decision-Making
3,
The Problem X has L possible states,{x(n)},n?(1,L)
The certainty distribution,{c(n)},n?(1,L)
The possible action strategy,{a(k)},k?(1,K)
The possible outcomes for each a(k),b(k,l)
c(1) … c( l) … c(L)
b(1,1) … b(1,l) … b(1,L)
b(k,1) … b( k,l) … b( k,L)
b(K,1) … b(K,l) … b(K,L)
a(1)
a(k)
a(K)
..,
..,
..,
..,
..,
..,
..,
..,
B(1)
B(k)
B(K)
..,
..,
Decision Matrix
Decision Tree
A,..
..,
..,
..,
...,..
...,..
a(1)
a(k)
a(K)
c(1)
c(L)
c(l)
c(1)
c(L)
c(l)
b(1,1)
b(1,l)
b(1,L)
b(k,1)
b(k,l)
b(k,L)
b(K,1)
b(K,l)
b(K,L)
Information-Based Decision Rules
For each a(k),define
x(k) = {c(l) t[b(k,l)] u[b(k,l)]}
={c(l)t(k,l)u(k,l)},l ? (1,L)
as the integrative utility of the action strategy a(k),
and then we have I( x(k) ) as the measure of
integrative pragmatic information of a(k),
The decision rule can thus be set to be the following,
If I( x(k’) ) = {I( x(k) )},
then a(k’) is chosen
Max
? k ? k’
4,
Unified Theory of Decision-Making
Information-Based Rule and Bayes Rule
Let t(k,l) = 1,?k,?l,we then have
x(k) = c(l) u(k,l)
I( x(k) ) can be reduced to ? c(l) u(k,l) l? (1,L)
The rule
If I( x(k’) ) = {I( x(k) )} Max ? k ? k’
Then a(k’) is chosen
Reduces to the well-known Bayes Rule,
Information-Based Rule and Min-Max Rule
If,further,let c(l) = 1,?l,then only u(k,l) needs to be
considered,Min-Max,Max-Min,Min-Min,Max-Max
are all special cases of this kind of rules,
u(1,1) … u(1,l) … u(1,L)
u(k,1) … u (k,l) … u (k,L)
u(K,1) … u(K,l) … u(K,L)
Summary
The essence of Decision-Making typically lies in the
information regeneration,from given information to
the wanted information -- strategic information as
was seen in section 1,
However,the current theories of decision-making are
much too simple,
The more advanced theory of decision-making will
further be discussed in Intelligence Theory,
Chapter 7
Information Regeneration
-- Decision Making Theory
List of Contents
1,From Knowledge to Strategy
2,Classical Model of Decision-Making
3,Information Theory of Decision-Making
4,Unified Theory
From Knowledge to Strategy
1,
Model of Information Regeneration
Information
Regeneration Knowledge
about the
Problem and
Environment
Strategy Information
for solving problem
under the given
environment
Goal to be sought
Knowledge and Strategy
Knowledge,A set of descriptions about the states
and the varying laws of the states
of certain categories of objects,
Strategy,A sequence of well organized action orders
for solving specific problems under certain
environment and certain goal,
Strategy can also be regarded as a special group of
information indicating the specific procedure of
problem solving,
Mechanism, from Knowledge to Strategy
P
Initial State
of Database Operation
New
State
Goal
Match
G
Rule
Base
Knowledge
Base
Rule
Sequence
N
Y
Strategy
Distance
Indication Control
E
Algorithm for Knowledge Activation
1,Given P(the Initial State of the Problem),E(the Knowledge
and the Rule Bases) and G(the Final State of the Problem)
2,Select the best Rule,from the Rule Base,so that whose left
side matches the Initial State while whose right side leads to
such a New State whose distance to the Goal is the minimum
compared with other selections by using the Knowledge
3,Check the New State thus obtained,If its distance to the
Goal is the smallest one but unequal to zero,do the same
thing from the New State as did in step 2
4,Otherwise,re-select a rule at step 2
5,Until the distance between the New State and the Goal
equal to zero,or sufficiently small,go loop from step 2 to 4,
The sequence of the rule applications is the strategy sought,
Classical Model of Decision-Making
2,
An Example,Umbrella Tricky
Benefits Table
Weather
Benefits
actions
Sunny Raining
Carry
a(1)
Not Carry
a(2)
p 1-p
c(1,1) c(1,2)
c(2,1) c(2,2)
Decision Rule
C(1) = p c(1,1) + (1-p) c(1,2)
C(2) = p c(2,1) + (1-p) c(2,2)
Calculate the average benefit for each action,
Choose the action with bigger benefit as the strategy,
If C(1) > C(2) then a(1) is chosen;
Otherwise,a(2) is chosen,
Model of Decision-Making
A(X) C
I(X;R)
DM
R
A(G)
G X
Information Theory of Decision-Making
3,
The Problem X has L possible states,{x(n)},n?(1,L)
The certainty distribution,{c(n)},n?(1,L)
The possible action strategy,{a(k)},k?(1,K)
The possible outcomes for each a(k),b(k,l)
c(1) … c( l) … c(L)
b(1,1) … b(1,l) … b(1,L)
b(k,1) … b( k,l) … b( k,L)
b(K,1) … b(K,l) … b(K,L)
a(1)
a(k)
a(K)
..,
..,
..,
..,
..,
..,
..,
..,
B(1)
B(k)
B(K)
..,
..,
Decision Matrix
Decision Tree
A,..
..,
..,
..,
...,..
...,..
a(1)
a(k)
a(K)
c(1)
c(L)
c(l)
c(1)
c(L)
c(l)
b(1,1)
b(1,l)
b(1,L)
b(k,1)
b(k,l)
b(k,L)
b(K,1)
b(K,l)
b(K,L)
Information-Based Decision Rules
For each a(k),define
x(k) = {c(l) t[b(k,l)] u[b(k,l)]}
={c(l)t(k,l)u(k,l)},l ? (1,L)
as the integrative utility of the action strategy a(k),
and then we have I( x(k) ) as the measure of
integrative pragmatic information of a(k),
The decision rule can thus be set to be the following,
If I( x(k’) ) = {I( x(k) )},
then a(k’) is chosen
Max
? k ? k’
4,
Unified Theory of Decision-Making
Information-Based Rule and Bayes Rule
Let t(k,l) = 1,?k,?l,we then have
x(k) = c(l) u(k,l)
I( x(k) ) can be reduced to ? c(l) u(k,l) l? (1,L)
The rule
If I( x(k’) ) = {I( x(k) )} Max ? k ? k’
Then a(k’) is chosen
Reduces to the well-known Bayes Rule,
Information-Based Rule and Min-Max Rule
If,further,let c(l) = 1,?l,then only u(k,l) needs to be
considered,Min-Max,Max-Min,Min-Min,Max-Max
are all special cases of this kind of rules,
u(1,1) … u(1,l) … u(1,L)
u(k,1) … u (k,l) … u (k,L)
u(K,1) … u(K,l) … u(K,L)
Summary
The essence of Decision-Making typically lies in the
information regeneration,from given information to
the wanted information -- strategic information as
was seen in section 1,
However,the current theories of decision-making are
much too simple,
The more advanced theory of decision-making will
further be discussed in Intelligence Theory,
