International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
procedure. Since its introduction (Zadeh, 1965), fuzzy logic was
applied to numerous problems and applications due to its ability
to provide a framework through which non-deterministic
problems could be addressed.
Fuzzy logic approach (Fuller, 2000) consists of five key
elements:
O Input fuzzification -is done through the definition of
functions that describe the degree of membership. It is
the measure of the fact that input belongs to a specific
fuzzy set. The set of input data can be assigned fuzzy
membership values.
OQ Application of fuzzy operators utilize the set of If -
Then rules that describe conditions (assumptions and
restrictions) between several input variables, a
conclusion regarding the membership of the output is
drawn and an output value is assigned.
OQ Definition of consequences - the membership function
of the output is obtained as a result of applying the
fuzzy operator. The consequence of this decision is
the retrieval of the fuzzy subset that corresponds to
the conclusion drawn using an implication operator.
O Aggregation of consequences — from each of the rules
stated a set of consequences is drawn. The
aggregation of these consequences provides the fuzzy
subset that result from these various rules.
Q Defuzzification — usually, it is required to draw one
single conclusion. In order to conclude a single
conclusion from the fuzzy process, it is then required
to select a representative element from the aggregated
fuzzy set.
Fuzzy decision
| cT
|
| re
input vector ]
|
| J
Figured. Fuzzified decision.
Fuzzy rules can be generated from examples using various
techniques. Kasabov presented a neural network approach for
generating fuzzy rules. Clustering technique and statistical
measures can also generate fuzzy rules. Decision rules work
well when input data is noise free.
Fuzzy logic has also been widely recognized as a powerful
scheme for decision-making processes in GIS. A high level of
complexity and varying level of structure and formalization
110
commonly characterize such processes. Moreover, multiple
objectives and constraints must be met
Fuzzy logic provides a powerful scheme in such decision-
making processes as it allows formulating loosely structured
expert knowledge. It should be noted that for this reason fuzzy
logic has also proven to be highly effective in quantitative as
well as qualitative decision making processes (Bolloju, 1995).
Applications of fuzzy logic for decision making and expert
knowledge systems have already been demonstrated in
environmental applications (Bolloju, 1995), semantic modeling
and reasoning (Benedikt et al., 2002), and land cover mapping
or categorical mapping (Zhang and Goodchild, 2002).
4. CONCLUSIONS
In this paper, the problem of the spatial data is addressed where
the contextual information is identified and temporal aspect of
spatial data is accounted. The running development of
information technologies, image processing techniques and
knowledge-based databases, together with the geographical
networks environment, will provide quite new and considerably
wider possibilities of using GIS. Our decisions are becoming
increasingly dependent on understanding of complex relations
and phenomena in the world around and GIS technology is able
to incorporate new requirements like decision tree context,
temporal aspects and fuzzy design. The main goal has been to
show selected aspects of this process and compare the
increasing possibilities of the sources with the difficulties of
data contextual structuring and the object history
implementation.
ACKNOWLEDGEMENT
The author would like to thank for the support from the research
project num. 102/04/0155 of the Grant Agency of Czech
Republic.
REFERENCES
[1] Benedikt, A, Reinberg, S., Riedl, L. 2002. A GIS
application to enhance cell-based information modeling.
Information Sciences 142(2002): 151-160.
[2] Bolloju, N., 1996. Formalization of qualitative models
using fuzzy logic. Decision support systems 17(1996),
275-289.
[3] Conners, R.W., Trivedi M.M, Harlow CH.A., 1984.
Segmentation of High-Resolution Urban Scene Using
Texture Operators, CVGIP 25, 273-310.
[4] Fuller R., 2000. /ntroduction to Neuro-Fuzzy systems.
Advances in soft computing, Physica-Verlag Heidelberg.
289 pages.
[5] Haslett J, 1985. Maximum likelihood discriminant
analysis on the plane using a markovian model of spatial
context, Pattern Recognition, vol. 18, no. 3, 287-296.
[10]
[11]
