1. Rajendra Akerkar
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2. Personalisation - user p
profile and p yp
prototypes
to provide: What is received is what is required
EXAMPLES
Web page retrieval to satisfy customer
Computer Interface
News Services Advertising
Services,
Regulation of messages -SMS. E-Mail
Personalised Data Mining
AI Machine Learning, Inference
and Linguistics provides the
intelligent agents for this
personalisation service
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3. message
P1 P2 P3 P4 P5 prototypes
s1 s2 s3 s4 s5 supports for interest
Personalised Fusion
Final Support s
send ? to user
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4. y y
Fuzzy Bayesian Nets
Fuzzy Decision Trees
Can we construct a theory
Fril programs of prototypes ?
Evidential Logic Rules
Can be have a theory of
Neural nets fusion ?
Fuzzy Conceptual graphs
Cluster over persons to get clusters for prototypes
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5. Data Base
WEB
answer fuzzy decision
tree
user query search agent
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6. Fril Evidential logic rule
x1 is g1 with weight w1 through
x2 is g w we g w
s g2 with weight w2 filt
class is f IFF
l i filter
. . . . h
xn is gn with weight wn
For input {xi = fi} f, gi, fi, h are fuzzy sets
Let i = Pr(gi | fi)
(g )
class is f with probability 
where
 =  h (w11 + w22 + … + wnn)
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7. Type company Random Variables
Offer LoanRate size company with conditional
Rate
age independencies
Rate Medical
Offer Comp
Su t
Suit Req
Suit Suit
S it
Company Size :
Loan Interest {large, medium, small}
{l di ll}
Time
Offer : {mortgage, personal loan, car loan, credit card
car insurance, holiday insurance, payment protection,
charge card, home insurance}
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8. Offer : {mortgage, personal loan, car loan, credit card
{mortgage loan loan
car insurance, holiday insurance, payment protection,
charge card, home insurance}
Type Rate : {fixed, variable}
LoanRate : {good, fair, bad}
Company Size : { g , medium, small}
p y {large, , }
Company Age : {old, middle, young}
Loan Period : {long, medium, short}
Rate Suitable : {very, average, little}
{very average
Company Suitable : {very, average, little}
Medical req : {yes, no}
Offer Suit : {good, av, bad}
Interest : {high, medium, low}
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9. X1 X2 X3
We update this prior
X5 joint distribution with
X4
respect to any given
tt i
variable instantiations
X6
n
P (X1 , ..., Xn )   P (X i | P
Pr(X Pr(X Parents(Xi ))
t (X Prior
i
i1
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10. C0 = {Offer*, LoanPeriod*, OfferSuit*}
C0 C1 = {OfferSuit,Offer, RateSuit}
C2 = {RateSuit*, LoanRate*, Offer, TypeRate*}
C3 = {CompSuit, MedReq,* OfferSuit, RateSuit
{CompSuit MedReq * OfferSuit RateSuit,
Interest*}
C1 C4 = {CompSize*, AgeComp*, CompSuit*}
C2 C3
C4
Compile Clique tree : equivalent to forming p
p q q g prior j
joint
distribution using an efficient message passing algorithm
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11. Message :
4% fixed rate long term mortgages available
from 40 year old fairly large Company FRIL
conceptual graph
graph instantiations
Offer = mortgage, Type rate = fixed, loan time = long
CompSize = dist, CompAge = dist.
Use message passing algorithm again to update clique distributions
with graph instantiations.
Result will be distribution over interest variable - defuzzify to
obtain degree of interest
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12. w1 w2 w3 w4 w5 w6 w7 X replaced with {wi}
1
We can also
fuzzify discrete
0 sets
X
Mass Assignment Theory provides:
{Pr(wi | x)} where x is point value, interval or fuzzy set
value
i.e we translate value on X to distribution over {wi}
Mass Assignment Theory provides:
Defuzzification: if {i} is distribution over {wi} then
x   i  i where i is expected value of wi
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i

13. medium
small large
0 1 2 3 4 5 6
DICE SCORE
Random Set of Voters x ≤3 4 5 6
% accept x as large % 0 20 80 100
large = 4 / 0.2 + 5 / 0.8 + 6 / 1
1 2 3 4 5 6 7 8 9 10
{6} : 0.2,
6 6 6 6 6 6 6 6 6 6 MAlarge ={5, 6} : 0.6,
5 5 5 5 5 5 5 5 {4, 5, 6} : 0.2
4 4
constant threshold : if voter accepts x and y>x then he must accept y
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14. weighted dice is small where small = 1 / 1 + 2 / 0.7 + 3 / 0.3
07 03
prior for dice : 1:0.1, 2:0.1, 3:0.5, 4 :0.1, 5:0.1, 6:0.1
MA = {1} : 0.3, {1, 2} : 0.4, {1, 2, 3} : 0.3
small
Pr(dice is x | small) = probability that a randomly chosen voter
chooses x as value of dice after being told dice value is small
h l f di f b i ld di l i ll
Least Prejudiced Probability Distribution for dice value =
1 : 0 3 + 0.2 + 0.3(1/7) = 0.5429
0.3 0 2 0 3(1/7) 0 5429
2 : 0.2 + 0.3(1/7) = 0.2429 Pr(x | small)
3 : 0.3(5/7) = 0.2143
For continuous fuzzy set we can derive a least prejudiced density
function whose expected value can be used for defuzzification
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15. What is Pr(dice is about_2 | dice is small) where
( )
about 2 = 1 / 0.5 + 2 / 1 + 3 / 0.5
small
0.3 0.4
04 0.3
03
{1} {1, 2} {1, 2, 3}
about_2 Prior
1/2(0.2) 1/7(0.15) 1 : 0.1
0
0 5 {2}
0.5 =01
0.1 = 0.0214
0 0214
2 : 0.1
3 : 0.5
0.15 0.2 0.15
0.5 { , ,
{1, 2, 3} 4 : 0.1
5 : 0.1
Pr(about_2 | small) = 0.6214 6 : 0.1
Point Semantic Unification used to determine Pr(f | g)
where f is fuzzy set, g is point, interval or fuzzy set
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16. prediction
output_sm output_me output_la Means of
output_sm,
output_me,
output me
output_la
are
mutually exclusive fuzzy sets on OUTPUT
t ll l i f t 1, 2, 3
input output_sm : 1
output {distribution over words} output me : 2
output_me
model
output_la : 3
Prediction = 11 + 22 + 33 Defuzzification
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17. Variable X - value x
V i bl l
x is point or fuzzy set defined on R
Bayes Node
Prior { }
{fi} Instantiate : Updated
Distribution {fi : P (fi | x)}
Pr(fi )} Distribution
NET
Classical probability theory does not allow
for this distribution update.
update
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18. P’
Updated
Distribution
o
on
Distribution Constraint X = (X1…Xn)
on Xk - D Minimum Relative Entropy
P
MIN
 ( )
Pr’(X)
Prior Pr’(X)
Distribution P'(X) Ln Pr(X)
on D satisfied
X = (X1…Xn)
var 1 distribution var 2 distribution
Prior Update Update
until convergence
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19. Bayes Net Compiled to give prior probability distributions.
Update Compiled Net with
input variables instantiated
to probability distributions using
relative entropy updating
Bayes Net message passing algorithms for
Clique tree updating modified to
be equivalent to this relative entropy updating
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20. Fuzzify :
A B C A : same as A above
B : {small, medium, large}
A : {a1, a2, a3} C : {low, av, high}
B : [1, 10]
[1 D : same as above
C : {1, 2, 3, 4, 5, 6}
D D : {d1, d2, d3} small medium large
A B C D
a1 x y {d1, d2} 1 10
 = Pr(medium | x)  = Pr(large | x)
low = 1 / 1 + 2 / 0.8 + 3 / 0.4
 = Pr(low | y)  = Pr(av | y)
av = 2 / 0.2 + 3 / 0.6 + 4 / 1 + 5 / 0.2
Pr(d1) = 0.5 Pr(d2) = 0.5
high = 5 / 0.8 + 6 / 1
08
Pr(small | x) = Pr(high | y) = 0
Note
x and y can be point values, intervals or fuzzy sets
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21. Reduced Data Base
Red ced Joint
Probability
A B C D Distribution
a1 medium low d1 .5
5
a1 medium low d2 .5
a1 large low d1 .5
a1 large low d2 .5
a1 medium av d1 .5
a1 medium av d2 .5
a1 large av d1 .5
a1 large av d2 .5
Repeat for all lines of database
Calculate Pr(D | A, B, C)
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22. 1. Search and Scoring based algorithms
1
2. Dependency Analysis algorithms Complexity
(a) n2
A. Node Ordering (b) n4
B.
B Without node ordering
Querying
Markov Cover :
Parents of query node + children of query
node + parents of these children
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23. ((prototype p1 (offer Mortgage) ) (evlog disjunctive (
(AgeOfCompany old_age) 0.1
(CompanySize large_size) 0.15
(LoanRate small rate) 0.4
small_rate)
(TypeRate quite_fixed) 0.1
(LoanPeriod long_period) 0.2
(MedicalRequired bias_to_yes) 0.05))) : ((1 1) (0 0))
((prototype p1 (offer PersonalLoan) ) (evlog disjunctive ( Rules can also
(AgeOfCompany old_age) 0.1 be used for
(
(CompanySize large_size) 0.15
p y g ) fusion
(LoanRate medium_rate) 0.4
(TypeRate quite_variable) 0.1
(LoanPeriod short_period) 0.2
(MedicalRequired bi t
(M di lR i d bias_to_no) 0.05))) : ((1 1) (0 0))
) 0 05)))
ETC - rules for other offers and other prototypes
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