Smart Shopper

A Consumer Decision Support System Using Type-2 Fuzzy Logic Systems

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].

Fuzzifier Inference

Rules

Defuzzifier

InputProcessing

OutputProcessing

Analyzer

(a)

CrispOutput

CrispInput

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].

1000

P2000

1

0,0

Low Medium High (a)

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.

CrispInput

Fuzzifier Inference

Rules

Type-Reducer

InputProcessing

OutputProcessing

Analyzer

Defuzzifier

(b)

CrispOutput

TypeReduced

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].

5

Q10

1

0, 0

Low Medium High (b)

Advantages for Type 2 FLS

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

0.5

x

1

1

0, 0 avg 1

1

0, 00.65

x = 0.65

(b)(a)

H

L

HL

avg

Special case: type-2 membership function is an interval set that the secondary membership function is either zero or one

Proposed Approach(1) Algorithm

= avg

L = avg -

H = avg +

(R) = (P) (Q) + (P) (Q)

5

Q

100, 0

1

Low Medium High

(Q) = 0.05

(R) = (P) (Q)

Proposed Approach(2) Type Reduce

5

Q

100, 0

1

Low Medium High

(R) = (P) (Qavg)

(R) = (P) (Qavg) + (P) (Q) = (P) (Q)

avg

5

Q

100, 0

1

Low Medium High

Proposed Approach(3)Results

0 2 4 6 8 100.0

0.2

0.4

0.6

0.8

1.0

HighMediumPoor

R

dr)r(

rdr)r(R AVG

dr)r(

rdr)r(*2R

R = Ravg R

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.

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