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3.4 Fuzzy Database Query Using Membership 
Functions Based on the Fuzzy Geometrical 
Partitions. 
In order to show the usefulness of the constructed membership 
functions in fuzzy query processing the new method was tested 
on a simulated database to determine value of the complex query 
objects "much greater than 5 and much less than 40" (Figure 
10) and "slightly less than 5 or slightly more than 5 and 
roughly equal to 5" (Figure 11). 
It must be noted that these kinds of queries cannot, in general, 
be solved by conventional database management systems 
because they require the interpretation of the fuzzy expressions 
"much greater than 5", "much less than 5", "slightly less than 
5", "slightly more than 5", and "roughly equal to 5". However 
using a fuzzy query processor the membership functions for 
these fuzzy expressions can be constructed and used as the 
basis for selecting valid database objects. 
  
1.04 
0.8 4 
0.6 4 
0.4 4 
MEMBERSHIP VALUE 
0.2 4 
  
  
  
0.0 y : a 
0 10 20 30 
DATABASE VALUE 
— >>5 
RR, 
««30 ee CS 30 and >> 5 
  
Figure 10: Selection of database values for the fuzzy 
query much more than 5 and much less than 40 
based on non-zero membership values. 
  
  
  
  
  
  
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0.0 pkey 
3 4 5 6 7 
DATABASE VALUE 
SLI > MFUN slightly greater than 5 
SL : M.FUN slightly less than 5 
ROUGHLY MFUN;2 TOughly equal to 5 
  
Figure 11: Fuzzy query selection for slightly less than 5 
or slightly more than and roughly equal to 5 using 
the intersection of the membership functions of the fuzzy 
query components. 
The selection of database objects satisfying complex fuzzy 
queries corresponds to the intersection of the fuzzy membership 
functions as shown graphically in Figures 10 and 11 for the 
fuzzy queries discussed above. In fuzzy sets literature the 
process of determining the (crisp) object satisfying the condition 
set out by the fuzzy sets intersection is referred to as 
defuzzification. One defuzzification strategy involves selection 
of the object corresponding to the centroid of the intersected 
region(s). 
183 
In General once the fuzzy membership functions are available 
standard fuzzy set theoretic operators can be used to solve the 
fuzzy query (see Kandel, 1986; Magrez and Smets, 1989; 
Zadeh, 1989). 
4. CONCLUDING REMARKS. 
A new method for representing and manipulating fuzzy 
information has been formulated and tested. It has been amply 
illustrated in the paper that this method differs substantially 
from the traditional approach of representing fuzzy linguistic 
variables. In particular this method makes it possible to define 
the meaning of fuzzy numerical restrictions in the domain of 
discourse by fuzzy geometric partitions of the search space. 
By means of geometric fuzzy partitions generic values of 
fuzzy numerical expressions can be constructed and used to 
facilitate comparison of fuzzy objects for database retrieval 
purposes. Alternatively it has been shown that geometric fuzzy 
partitions can form the basis for constructing reasonable 
membership functions for characterizing fuzzy numeric 
expressions. 
The usefulness of fuzzy membership functions generated from 
fuzzy geometric partitions in fuzzy query processing was 
illustrated for a model database. In addition a fuzzy comparison 
operator based on the fuzzy geometrical partitioning of the 
search space was designed and implemented in an experimental 
knowledge based system. 
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