MEMBERSHIP VALUE 
  
  
  
1.0 j 
0.8 1 
os- 
0.4 J 
02 
0.0 + T T 
4 5 6 
DATABASE VALUE 
ABOUT M.FUN,1 about 5... (1) 
ABOUT M.FUN,2 about 5 … (2) 
Figure 6: Membership Function for about 5; 
Two interpretations. 
1.04 
054 
os] 
o4 
02- 
0.0 mL. T—À— 
4 5 6 
  
MEMBERSHIP VALUE 
  
  
  
  
  
1.0 4 
0.8 4 
0.6 4 
0.4 + 
MEMBERSHIP VALUE 
0.2 - 
  
  
  
0.0 Y ; : 
3 4 5 6 7 
DATABASE VALUE 
——— ROUGHLY M.FUN, 1 roughly equal to 5 .... (1) 
ROUGHLY M.FUN2 roughly equal to 5 .... (2) 
  
Figure 8: Membership function for roughly equal to 5; 
Two interpretations. 
  
  
  
  
DATABASE VALUE 
IDENTIFY FUZZY OBJECT IDENTIFY FUZZY OBJECT 
sm > OR<M.FUN,1 More or less 5 ... (1) EXTRACT FUZZY VALUE EXTRACT FUZZY VALUE 
» OR « MFUN2 more or less 5.... (2) CREATE GENERIC VALUE CREATE GENERIC VALUE 
  
  
  
  
  
  
   
  
  
  
  
  
  
Figure 7: Membership function for more or less 5; 
Two interpretations. 
  
   
  
MATCH GENERIC VALUES 
  
   
Figure 9: Design of the FUZZ subsystem for processing fuzzy query. 
membership functions that the fuzzy partitions based 
representation of fuzzy numeric expressions produces 
membership functions similar to those produced by using 
standard membership functions. For comparison purposes 
reference can be made to Zadeh et al. ( 1975), Mizumoto and 
Tanaka (1975), Dubois and Prade (1980), Chen (1985), Kandel 
(1986) and Dubois and Prade (1988). 
3.3 Fuzzy Database Query Using Generic Values 
Derived From the Fuzzy Geometric Partitions. 
Fuzzy database retrieval requires the solution of two different 
problems. The first problem arises when a vague, or fuzzy, 
query is placed to a database containing precise, well defined, 
data or facts. The second problem concerns retrieval of precise 
queries placed to a fuzzy database. The concept of the generic 
value of a fuzzy numeric expression, introduced at the 
beginning of section 3, has been used to design a fuzzy 
comparison operator capable of solving the two problems, and 
therefore, capable of fuzzy database retrieval. 
The design of the operator, called FUZZ(Mtalo, 1990), is 
shown in Figure 9. Using this operator both the fuzzy query 
and fuzzy database object are parsed into atomic fuzzy 
components which are then transformed into generic values for 
database matching purposes. If the query and database object 
currently being examined are both non-fuzzy the operator uses a 
simple database matching procedure, otherwise the operator 
182 
generates and compares upper and lower bounding generic 
values to determine the matching object(s). 
To ensure that borderline cases are not rejected offhand, the 
crisp interval represented by the upper and lower bounding 
generic values is "fuzzified" by allowing values slightly greater 
or slightly less than the computed generic values into the set of 
possible database objects. This allows queries not precisely 
matching the specifications of database objects to be processed. 
The retrieval of fuzzy queries based on the concept of generic 
values must be regarded as an approximate method since it 
resorts to interval comparison. However vague user queries 
reflect a degree of uncertainty about what the user wishes to 
retrieve. Similarly fuzzy data reflects uncertainty about the 
information stored in the database. Under these circumstances 
the proposed method provides a simple and convenient way to 
represent and manipulate the uncertainty inherent in vague 
queries and fuzzy database information. Where more accuracy 
in the representation of uncertainty is needed fuzzy operators, 
based on the fuzzy set theory, must be used as elucidated in 
Dubois and Prade (1988), Kandel (1986) and other literature.