Fuzzy Information Retreival Methods

    Fuzzy retrieval methods are a radical new technique which was introduced to compensate the limitation of traditional boolean and vector methods which could not take user's preference into account. Many times the user query is fuzzy as he himself doesn't know much about the subject. At such times the traditional 1-0 logic of boolean methods or vector logics don't work out and the documents returned might either be too many or too few. To offset this problem, fuzzy techniques were introduced.
    In this blog, I will try to introduce the logic of fuzzy sets and then we will see how fuzzy information retrieval methods work.

Fuzzy sets:

    Traditional sets theory follow boolean logic with elements either being or not being part of the sets. But with fuzzy sets an element can belong to a set partially. Here, an element belongs to a set with varying degree between 0 and 1.
Thus we can define membership function in fuzzy sets as:
Let ,
    set U={x1,x2,x3,....,xn}=universe of discourse (set of all elements)
    function m=membership function
then for each element x in U,
    x is not included if m(x)=0
    x is included if m(x)=1
    x is partially included if 0<m(x)<1
and function :
d_{(a and b)}=min(d_a,d_b)
or function:
d_{(a or b)}=max(d_a,d_b)
   
Fuzzy Information retrieval methods:

The two famous fuzzy retrieval models are:

1. The MMM model
2. The Piace model

•    The MMM (Mixed Min and Max) model: 

     In MMM each term has a document weight fuzzy set corresponding to it. It considers only minimum and maximum values while calculating document similarity. Since the two main functions used in queries are "and" and "or" functions, the document similarities are resolved as:
        
SlM(Q_or, D) = C_or1 * max(d_A1, d_A2, ..., d_An) + C_or2 * min(d_A1, d_A2, ..., d_An)
SlM(Q_and, D) = C_and1 * min(d_A1, d_A2, ..., d_An) + C_and2 * max(d_A1, d_A2 ..., d_An)

where C_or1,C_or2,C_and1 and are constants such that:

    C_or2=1-C_or1
    C_and2=1-C_and1
 

•   Piace Model

      The Piace Model is an extention of the MMM model where instead of taking just minimum and maximum we consider all terms. The equation is:

 

 

 

Here, r is a constant usually set to 1 for and and 0.7 for or queries and w's are the document weights arranged in descending order for or queries and ascending for and queries. 

Thus the fuzzy techniques are a relatively new method used to cater to user requirement implemented in the above methods.

References:

(1)https://en.wikipedia.org/wiki/Fuzzy_set

(2)https://en.wikipedia.org/wiki/Fuzzy_retrieval

(3)http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1411824