fuzzy model
Introduction
Fuzzy recovery techniques are based on the Extended Boolean Model and Fuzzy Set theory.
There are two classic fuzzy recovery models: Mixed Min and Max (MMM) and the Paice model. Both models do not provide a way for the weighted evaluation of queries, which is considered by the P-norm algorithm.
Mixed Minimum and Maximum Model (MMM)
In fuzzy set theory, an element has a varying degree of membership, say d, to a given set A rather than the traditional membership option (is an element/is not an element).
In the MMM[1]
Each indexed term has an associated fuzzy set. The weight of a document with respect to an indexed term A is measured by the degree of membership of the document in the fuzzy set associated with A. The degree of membership for the union and the intersection is defined in fuzzy set theory as follows:.
According to this, the documents that should be retrieved for a query of the form A or B, should be in the fuzzy set associated with the union of the two sets A and B. Similarly, the documents that should be retrieved for a query of the form A and B must be in the fuzzy set associated with the intersection of the two sets. Therefore, it is possible to define the similarity of a document for the query o as max(d, d) and the similarity of a document with the query y as min(d, d).
The MMM model attempts to smooth out the Boolean operators by considering the query-document similarity as a linear combination of the minimum and maximum of the document weights.
Given a document D with the weights of the indexed terms
d, d, ...,
d for terms A,
A, ..., A*, and the*
queries:.
Q = (A or
A or ... or A)
Q = (A y
A and ... and A).
The document-query similarity in the MMM model is calculated as follows:.
SlM(Q, D) = C *