International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
contractility changes with the velocity or the distance. The 
time is relative, and different inertia system has different time 
coordinates. Furthermore, the time of an inertia system may 
find that the time of another inertia system opposite is slower. 
Because of time expansion, the observed time is always bigger 
than the true time. 
2. SUBJECTIVE COGNITION 
Compared with the complexity of the real world, the ability of 
human cognition is very limited at present. In order to guide 
their lives in the context of needs and wishes, people try to 
make sense of the real world around themselves in terms that 
they can understand and manipulate (Figure 2). First, they 
understand the spatial entity in the world, define and generalize 
the spatial entity, observe the spatial entity, relate the 
observations to an established conceptual data model, represent 
the spatial data in formal term, and store the data in the 
computerized machine. Some entities are perceived rather than 
the real entities, e.g., subjective neighbourhoods. Then, they 
edit, retrieve and analyze the spatial entities on the basis of the 
stored data with the computerized GIS. When cartographers 
perform generalization operations, such as aggregating, 
amalgamating and merging on features, other category features 
may be grouped into a certain feature. 
  
Figure 2 objective cognitions 
As the entity is complex and changeable in the real world, 
people have to select the most important spatial aspects to 
approximately approach the reality entity. All spatial data are 
acquired with the aids of some theories, techniques and 
methods that specify implicitly or explicitly the required level 
of abstraction and generalisation (Miller, Han, 2001). So the 
depicted data are less than the total data about the spatial entity, 
and only an essential part of the real variation is described. 
The desired level is closely related to the spatial nominal 
concept of perceived reality, and it is defined by database 
specification of human cognition. In fact, the desired level is 
also the constraints from the current limitation of people 
cognition, and the spatial database composed of the captured 
data is only an abstracted representation. In consequence, the 
computerized entities may lose some aspects of the real entities, 
which make some uncertainties go along with spatial databases. 
Take the imagery data in remote sensing for example, the 
262 
incomplete definitions of soil and forest may result in the 
vagueness about exactly what is their boundary in the ground. 
3. APPROXIMATE TECHNIQUES 
The observer cannot perceive the spatial of uncertain spatial 
entity directly, but only after they have been filtered by the 
uncertainty theories (Zimmermann, 2001). Based on the 
human cognition, the spatial entities in the real world are 
mapped to the crisp spatial objects in the computerized 
database via the given techniques for formal modeling, 
reasoning and computing (Figure 3). And the stored spatial 
objects are digitally represented with spatial data and their 
spatial relationships in a spatial database (Shi, Wang, 2002). 
Because the entity is indeterminate while the techniques are 
often deterministic (Burrough, Frank, 1996), the traditional 
techniques are often problematic when they are used to handle 
the spatial uncertainty. 
First, most of the traditional tools are crisp, deterministic, 
precise, and dichotomous character. In dual logic, a 
proposition is “true or false" and nothing in between, in set 
theory, an element either belongs to a set or not rather than 
*more or less", and in optimization, a solution is either feasible 
or not (Zimmermann, 2001). They have implicitly assumed 
that the spatial entities are determinate or homogeneous, which 
is often not true in the real world (Figure 3). The acquired data 
via mathematical techniques are not as well as the real 
attributes in the world. For example, probability theory and 
fuzzy sets both integrate set theory and predication equation, 
and map the uncertainty to a numerical value in the interval [0, 
1] in order to abstractly approach the spatial entity in the real 
world (Wang, Shi, Wang, 2003). 
  
Point obiect 
rn. 
Line object 
Area object 
Spatial complex 
Figure 3. Approximate techniques 
Second, no one solution can handle the complex interaction of 
different types of uncertainty. Each solution is capable of 
assessing just some aspects of uncertainty. The existing 
method on uncertainty often models a specific type of 
uncertainty under the specific type of circumstances, e.g., the 
theory of fuzzy sets can only model the fuzzy uncertainty. 
Third, some techniques are incomprehensible to most common 
users without the background-associated knowledge, even 
some decision-makers. They may be unaware of, even misuse 
of the accuracy descriptors such as reliability diagrams and 
position error estimation on the basis of probability theory and 
   
    
  
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