1 A Fuzzy Logic Framework for Web Page Filtering Authors ： Vrettos, S. and Stafylopatis, A. Source ： Neural Network Applications in Electrical Engineering, NEUREL ' th Seminar on, Sept. 2002,Page(s): Present by ： Chung - Hsun Hsieh Members: Chung - Hsun Hsieh & Wen - Lin Lee Date:2003/12/23

2 Outline Introduction Textual Retrieval through Rocchio ’ s Algorithm Fuzzy logic Framework Conclusion

3 Introduction This paper propose a framework that uses fuzzy logic to combine available text classifiers in a user friendly and common sense manner. Each classifier is considered to be a membership function that provides the membership degree of a certain page to a class.User use a logical rule combining the available classes,e.g.(class1 AND class2) OR class3.

4 Textual Retrieval through Rocchio’s Algorithm(1/4) When the case is the retrieval of textual objects, like text documents or HTML pages, these objects are usually represented as vectors in the vector space language model(VSM). A document collection of d documents and t terms is represented as a t*d term-by-document matrix A. the columns of A are the document vectors the rows of A are the term vectors.

5 Textual Retrieval through Rocchio’s Algorithm(2/4) The elements of the matrix A are often weighted by a two- components transformation - :the global weight of the i-term in the collection - :the local weight of the i-term in the j-document Document j Term i

6 Textual Retrieval through Rocchio’s Algorithm(3/4) A query is represented as a vector in the same vector space. A document is retrieved when it contains one or more terms of this query vector. The retrieved documents are then sorted according to the cosine similarity measure between the document and the query vector: For j= i,….,d where the Euclidean vector norm is defined as for vector x.

7 Textual Retrieval through Rocchio’s Algorithm(4/4) Rocchio’s algorithm learns a model for every category by combining document vectors into a prototype vector which may be the sum or the average of the documents that belong to the category: -NC:the number of documents that belong to category set C - :document vector - :prototype vector

8 Fuzzy Logic(1/3) Let X be a space of objects and x be an element of X. A classical set A is defined as a collection of element x € X, such that each x can either belong or not belong to the set A. We can represent a classical set A by a set of ordered pairs (x,0) or (x,1), which indicates that x  A or x€A.

9 Fuzzy Logic(2/3) A fuzzy set is defined as a set of elements that may belong to the set by a membership degree value between 0 and 1. A fuzzy set A in X is defined as a set of ordered pairs A={(x,ų(x)),x€A},where ų(x) is called membership function(MF) for the fuzzy set A.

10 Fuzzy Logic(3/3) The union, intersection, complement of two fuzzy sets A and B is a fuzzy set C,denote C=A  B or C=A OR B, C=A  B or C=A AND B,  A,whose MF is related to those of A and B by ųC(x)=max(ųA(x), ųB(x))= ųA(x)  ųB(x)…….(1) ųC(x)=min (ųA(x), ųB(x))= ųA(x)  ųB(x)…….(2) ų  A(x)=1-ųA(x)…………………………………………(3)

11 Framework(1/2) If is the prototype vector of the topic and is a web page, then the membership function of the topic is defined to be: We are able to use ųC as a membership function due to the fact that 0  ųC  1, because both and are positive vector.

12 Framework(2/2) Once we have related each available topic with its corresponding membership function,we are able to formulate and evaluate logical expressions of the form e.g. (Topic1 AND Topic2) OR NOT (Topic3) using fuzzy logic operators, eq. (1)(2)(3)

13 Interface

14 Conclusions This paper has presented a framework that makes possible the use of fuzzy logic in web filtering. Based on this, an interface for web filtering has been materialized using the directory structure of Open Directory Project. Through the interface, the user formulates fuzzy rules using the available categories resulting in different orderings of the retrieved sets.

15 ~The End~