Fuzzy Logic Information Retrieval Model

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Fuzzy Logic Information Retrieval Model
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Fuzzy Logic and Information Retrieval.

• Fuzzy sets, fuzzy reasoning, null values.
• Fuzzy logic in information retrieval.
• Fuzzy query, retrieval process.
• Common objections to fuzzy logic.
• Conclusion.

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Theory of Fuzzy Logic
  Lotfi Zadeh introduced the theory of Fuzzy
Logic in his paper, Fuzzy Sets (1965).   Fuzzy
Logic provides a method of reducing as well as
explaining the system complexity
The Idea of Fuzzy Sets   Fuzzy sets are
functions that map a value, which might be a
member of a set, to a number between zero and
one, indicating its actual degree of
membership A degree of zero means that the
value is not in the set, and a degree of one
means that the value is completely representative
of the set.
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 Characteristic Function Conventionally we can
specify a set C by its characteristic function,
Char C(x). If U is the universal set form which
values of C are taken, then we can represent C
as   C x x ? U and Char C(x) 1   This
is the representation for a crisp or non-fuzzy
set. For an ordinary set C, the characteristic
function is of the form  
Char C(x) U ? 0,1   However for a Fuzzy set A
we have   Char F(x) U ?
0,1 That is, for a fuzzy set the characteristic
function takes on all values between 0 and 1 and
not just the discrete values 0 or 1.   For a
fuzzy set the characteristic function is often
called the membership function and denoted by
?F(x)
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  An example   By using conventional method we
can call a person TALL if the height is 7 feet
and a person with height 5 feet is NOT TALL. That
is we represent the person is either TALL or
NOT TALL in Boolean Logic 1 or 0, 1 for TALL
and 0 for NOT TALL   Fuzzy sets may be used to
show the relationship or degree of precision
  If S is the set of all people in the
Universe, a degree of membership is assigned to
each person in set S to find the subset
TALL.   The membership function is based on the
persons height.   TALL(x) 0,
if Height(x) lt 5,
(Height(x)
5 )/ 2 if 5lt Height(x) lt 7
1,
if height(x)gt 7
feet
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Degree of relationship
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Benefits of Fuzzy System Modeling
  Ability to Model Highly Complex
Business Problems Ability to Model
System Involving Multiple Experts Reduce
Model Complexity Improve Handling of
Uncertain and Possibilities
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Fuzzy Logic in IR
Fuzzy Model Overview   A fuzzy model, like
traditional Expert and Decision Support System,
is based on the input, process, output flow
concept.   A fuzzy model differs in two
important properties What flows into and out of
the process, and the fundamental transformation
activity embodied in the process itself
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Information flow in Fuzzy System
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Basic Fuzzy Databases Approaches
Fuzzy Relation   A fuzzy relation is a subset
of the set corss product P(D1) X P(D2) X X
P(Dm) Membership in a specfic relation, r, is
determined by the underlying semantics of the
relation.
Fuzzy Tuples and Interpretation   A fuzzy tuple
t, is any member of both r and P(D1) X
P(D2)XXP(Dm)
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The simplest form for a fuzzy database is the
attachment of a membership value ( numeric or
linguistic ) to each tuple.   For a query
POLLUITED_SITE, the membership values denotes the
degree to which the tuple belongs within the
relation. Each tuple corresponds to a site and
its particular major source of pollution
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POLLUTED_SITE  
               
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QUERY1 What are the opinion of the resident F on
environmental effects of pollutant?   R1 ( ? (
POLLUTANT, EFFECT) ( ?( NAME F) (SURVEY) )
    This yields the temporary relation R1   R1
Oil Severe, Dioxin Extreme, Water
Tolerable
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SURVEY    
  Querying Fuzzy Relational Databases   In
systems that are relationally structured and
using fuzzy set concepts, nearly all
developments have considered various extensions
of the relations algebra.
 
 
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Data Storage and Retrieval Process   When a query
is made for the address of a Person the archived
data is clustered according to the various
criteria, e.g., by similar street names, within
the same zip code or by similar last name   It
constructs and attaches to a window discription a
set expression for which an example   (Cluster1 ?
Cluster3) ? ( Cluster2 ? Cluster3)   Several
properties of clusters are relevant. Each Cluster
entry is a key value followed by a set of
archived record numbers.
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Example   If the destination is city is
unambiguous and if Plz is detected as part of a
street name, There might exist a cluster
classified among other destination city clusters
and whose key entries are street names and
abbreviations   The contents of this cluster
might appear as   Pizza / 50873, 109234,
231709 Place / 25670, 43831, 331992 Plaza /
12909, 234144.   Given the Plz example just
shown, each of the key match to a certain
extent. One measure of how well each matches is
based on the number of changes necessary to copy
a prefix of the key in the cluster entry onto
the detected street name.
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Common Objections to Fuzzy Logic

• Much of the opposition to fuzzy logic is based on
  the misconception
• Fuzzy logic invites the belief that the modeling
  process generates imprecise answers

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Conclusion

• The exact directions and extent of future
  developments will be dictated by advancing
  technology and market forces
• Fuzzy logic is a tool and can only useful and
  powerful when combined with Analytical
  Methodologies and Machine Reasoning Techniques