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

Ling Gu 2003 Fall CSc8810

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**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

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**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.

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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.

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**Type-1 Fuzzy Logic Systems**

Type-1 fuzzy sets represent uncertainty by numbers in the range [0, 1]. Fuzzifier Inference Rules Defuzzifier Input Processing Output Analyzer (a) Crisp

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**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 P 2000 1 0,0 Low Medium High (a)

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**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. Crisp Input Fuzzifier Inference Rules Type-Reducer Processing Output Analyzer Defuzzifier (b) Type Reduced Set

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**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 Q 10 1 0, 0 Low Medium High (b)

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**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.

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**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 0.5 x 1 0, 0 avg 0.65 x = 0.65 (b) (a) H L

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**Proposed Approach (1) Algorithm**

= avg 5 Q 10 0, 0 1 Low Medium High (Q) = 0.05 L = avg - H = avg + (R) = (P) (Q) (R) = (P) (Q) + (P) (Q)

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**Proposed Approach (2) Type Reduce**

5 Q 10 0, 0 1 Low Medium High avg Low Medium High 1 Q 0, 0 5 10 (R) = (P) (Qavg) (R) = (P) (Qavg) + (P) (Q) = (P) (Q)

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**Proposed Approach (3)Results**

R = Ravg R

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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.

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**Smart Shopper User Interface(1)**

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**Smart Shopper User Interface(2)**

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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.

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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.

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**Future Work Use the generation of membership functions.**

More type-2 variables. Weight function. Interval inputs to improve the system.

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REFERENCES [Jang97] Jang, J-S. R., C-T. Sun, and E. Mizutani, "Neuro-Fuzzy and Soft Computing", Prentice Hall, 1997. [Liang00] Liang, Q.L. and J.M. Mendel, "Interval Type-2 Fuzzy Logic System: Theory and Design", IEEE Transaction on Fuzzy System, 8, (2000). [Kamik99] Kamik, N.N., J.M. Mendel, and Q.L. Liang, "Type-2 Fuzzy Logic System", IEEE Transaction on Fuzzy System, 7, (1999). [Popp96] Popp, H. and D. Lodel, "Fuzzy Techniques and User Modeling in Sales Assistants", User Modeling and User-Adapted Interaction, 5, pp (1996). [Roussinov01] Roussinov, D.G. and H-C. Chen, "Information navigation on the web by clustering and summarizing query results", Information Processing and Management, 37, pp (2001). [Yager88] Yager, R.R., "On ordered weighted averaging aggregation operators in multicriteria decisionmaking", IEEE Transactions on systems, man and cybernetics: Part A, 18, pp (1988). [Zadeh75] Zadeh, L.A., "The Concept of a Linguistic Variable and its Application to Approximate Reasoning - I", Information Sciences, 8, pp (1975). [Zadeh01] Zadeh, L.A., "Letter to the members of the BISC group", in: Proceedings of the BISC Int. Workshop on Fuzzy Logic and the Internet, 2001. [Zhang03] Zhang, Y-Q., "Fuzzy Logic, the Internet and E-Commerce", In: Fuzzy Web Shopping Agents, 2003.

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