International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
given continuous attribute data into discrete values. and this 
operation may be a main origins of uncertainties in the whole 
process of spatial knowledge discovery. At this phase, a lot of 
uncertainties may be eliminated by uncertainty handling 
techniques but never completely, even some new uncertainties 
will be produced in handling process due to impropriety of the 
techniques. 
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Uncertainties from data mining mainly refer to the limitation of 
mathematical models, and mining algorithm may further 
propagate, enlarge the uncertainty during the mining process. 
Spatial knowledge representation exists in uncertainties, 
including randomness, fuzziness and incompleteness. To a same 
knowledge, it may be represented by different methods. Most of 
spatial knowledge discovered by spatial data mining is 
qualitative knowledge and the best way to represent them is the 
natural language. 
   
    
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Figure 2. Uncertainties and its propagation in the process of spatial knowledge discovery 
4. SPATIAL KNOWLEDGE DISCOVERY BASED ON 
FUZZY EVIDENCE THEORY 
4.1 About the Evidence Theory 
Evidence theory, namely Dempster-Shafer (D-S) theory, aims 
to provide a theory of partial belief, which extend traditional 
probability theory. Firstly, we should briefly introduce the 
evidence theory. 
The frame of discernment, © , is the set of mutually exclusive 
and exhaustive propositions of interest. Defined on the set of 
subsets of © is the basic probability assignment or mass 
function, m, that associates with every subset of © a degree of 
belief that lies in the interval [0, 1]. Mathematically, m is 
defined as follows: 
m:29 [0,1] (2) 
such that: 
m(d)=0 (3) 
> m(x) il (4) 
«co 
A Belief function: 
Bel( A) = > mB) (5) 
BoA 
A Plausibility function: 
PI( A) = 1— Bel(+A) = > m(B) (6) 
BOAD 
Thus, at any given time the interval [ Be/( A), P/( A) ] defines 
the uncertainty associated with A. While Bel(A) is the 
definite support for A, P/(A) is the extent to which the 
evidence at that present time fails to refute A. 
When identify an object. all evidences associated with the 
object must be combined. The Rule for the combination of 
evidence (the Orthogonal Sum, © ): 
se m, (A)m, CB) 
4nriB 
ls > om, (A)ym,(B) 
Ao Bzo 
(mm, Dm, )(c) = (7) 
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