### Type-2 Fuzzy Logic System

```Smart Shopper
A Consumer Decision Support System
Using Type-2 Fuzzy Logic Systems
Ling Gu
2003 Fall
CSc8810
Outline
 Decision Support System
 Why Fuzzy Logic System
 Type-1 Fuzzy Logic Systems and
membership function
 Type-2 Fuzzy Logic Systems and
membership function
 Proposed Approach
 Implementation
 Discussion and Conclusion
 Future Work
Decision support systems
 The consumer decision support
systems is to extract products that
match users’ queries, and filter out
unmatched products.
 The match is measured by a ranking
function.
 The filtering function calculates the
ranking of each product and filters
out the lower ranked products.
Why Fuzzy Logic System
 The fuzziness nature of the e-commerce
makes the ranking process much more
difficult.
 User's queries are often complex and fuzzy.
 They are contradictory and need to be
balanced
 The general framework of fuzzy
reasoning allows handling of this
uncertainty.
Type-1 Fuzzy Logic Systems
 Type-1 fuzzy sets represent uncertainty by numbers in the
range [0, 1].
(a)
Input
Processing
Rules
Output
Processing
Crisp
Input
Crisp
Output
Fuzzifier
Inference
Analyzer
Defuzzifier
Type-1 Membership Function
 Two-dimension in which each element of the type-1 fuzzy set has a
membership grade that is a crisp number in [0, 1].

Low
Medium
High
(a)
1
0,0
1000
2000
P
Type-2 Fuzzy Logic Systems
Type-2 fuzzy sets are an extension of type-1 fuzzy sets in which
uncertainty is represented by an additional dimension.
(b)
Input
Processing
Rules
Output
Processing
Crisp
Output
Defuzzifier
Crisp
Input
Fuzzifier
Inference
TypeReducer
Analyzer
Type
Reduced
Set
Type-2 Membership Function
 Three dimensions in which each element of the type-2 fuzzy set has
a membership grade that is a fuzzy set in [0, 1].

Low
Medium
High
(b)
1
0, 0
5
10
Q
 This extra third dimension in type-2 fuzzy logic systems
(FLS) gives more degrees of freedom for better
representation of uncertainty compared to type-1 fuzzy sets.
 Type-2 fuzzy sets are useful in circumstances where it is
difficult to determine the exact membership function for a
fuzzy set.
 Using type-2 FLS provides the capability of handling a
higher level of uncertainty and provides a number of
missing components that have held back successful
deployment of fuzzy systems in human decision making.
Interval Type-2
Membership Function
Special case: type-2 membership function is an interval set that the
secondary membership function is either zero or one

(b)
(a)
1
1
avg
H
x = 0.65
L

x
0, 0
0.5
0.65
1
0, 0
L
avg
H
1
Proposed Approach
(1) Algorithm
 = avg  

L = avg - 
1
Low
Medium
High
(Q) = 0.05
H = avg + 
Q
(R) = (P) (Q)
0, 0
5
(R) = (P) (Q) + (P) (Q)
10
Proposed Approach
(2) Type Reduce

Low
Medium
High
1
avg
Low
Medium
High
1
Q
0, 0
5
10
Q
0, 0
5
10
(R) = (P) (Qavg)
(R) = (P) (Qavg) + (P) (Q) = (P) (Q)
Proposed Approach
(3)Results
1.0
R AVG  
0.8
Medium
Poor
( r )rdr
High
R  2 * 

0.6
 (r )dr
( r )rdr
 (r )dr
0.4
R = Ravg  R
0.2
0.0
0
2
4
6
R
8
10
Implementation
 Java servlet is used to implement this
type-2 FLS-based consumer decision
support system.
 Two inputs: one (price) uses type-1,
the other (quality) uses type-2.
 The result (rank) is a fuzzy set and
ranges from the low limit to the high
limit.
Smart Shopper User Interface(1)
Smart Shopper User Interface(2)
Discussion
 A better results might be obtained by
defined the membership function of
price also to be type-2.
 It is important to define reasonable
membership functions.
 Using an interval input for the price,
which provides more freedom for users.
 Provide a weight function.
Conclusion
 An up-low limit method has been
proposed to handle the complex
calculations of type-2 FLS.
 This approach reduces the complex
calculations of type-2 to type-1.
 A fuzzy output of an interval type-2 FLS
can be obtained using the up-low limit
technique. This fuzzy output provides
more reasonable conclusion for the
users.
Future Work
 Use the generation of membership
functions.
 More type-2 variables.
 Weight function.
 Interval inputs to improve the system.
REFERENCES
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DEMO
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