6
A. Salski
Compared to conventional classification methods fuzzy clustering methods
enable a better interpretation of the data structure.
Spatial data is an essential part of ecological data. The fuzzy extension of the
interpolation procedure for spatial data, the so-called fuzzy kriging, can be
mentioned as an example of fuzzy approach to spatial data analysis (Bardossy
1989; Diamond 1989; Piotrowski et al. 1996). Fuzzy kriging is a modification of
the conventional kriging procedure; it utilizes exact (crisp) measurement data as
weIl as imprecise estimates obtained from an expert and defined as fuzzy
numbers. Regionalization of ecological parameters based on fuzzy kriging reflects
better the imprecision of input data.
Fuzzy knowledge-based modelling can be particularly useful where there is no
analytical model of the relations to be examined or where there is an insufficient
amount of data for statistical analysis, or where the degree of uncertainty of these
data is very high (Salski 1992; Salski et al. 1996; Li 1996; Daunicht et al. 1996;
Bardossy and Duckstein 1995; Pedrycz 1996; Bock and Salski 1998). In these
cases the only basis for modelling is the expert knowledge, which is often
uncertain and imprecise.
1.3
Fuzzy Classification: A Fuzzy Clustering Approach
Conventional clustering methods definitely place an object within only one
cluster. With fuzzy clustering this is no longer essential, since the membership
value of this object can be split up between different clusters. In comparison to
conventional clustering methods the distribution of the membership values
provides additional information - the membership values of a particular object can
be interpreted as the degree of similarity between this object and the respective
clusters (Salski and Kandzia 1996).
Classifying existing chemicals according to their ecotoxicological properties
(Friederichs et al. 1996) can be taken as an application example of the fuzzy
cluster analysis. The large number of existing chemicals makes it necessary to
select representative chemicals which reflect the relevant properties of possibly a
major group of compounds. Therefore the main tasks of this application are:
- to find distinguishable clusters with characteristic properties,
- to find chemicals representative for each cluster,
- to examine the role of different parameters for clustering.
Compared to conventional clustering methods the fuzzy clustering technique is
more appropriate to handle the uncertainty of ecotoxicological data, which results,
for example, from the difficult comparability of these data. The analysis of the
partition efficiency indicators was used to choose the fuzzifier value and the
determination of the optimal number of clusters, e.g.:
- partition entropy (should be minimal),
- partition coefficient, where values closer to I indicate the "better" partition,
- non-fuzziness index, indicating the "best" partition by the highest value,
independently of the number of clusters.
A. Salski
Compared to conventional classification methods fuzzy clustering methods
enable a better interpretation of the data structure.
Spatial data is an essential part of ecological data. The fuzzy extension of the
interpolation procedure for spatial data, the so-called fuzzy kriging, can be
mentioned as an example of fuzzy approach to spatial data analysis (Bardossy
1989; Diamond 1989; Piotrowski et al. 1996). Fuzzy kriging is a modification of
the conventional kriging procedure; it utilizes exact (crisp) measurement data as
weIl as imprecise estimates obtained from an expert and defined as fuzzy
numbers. Regionalization of ecological parameters based on fuzzy kriging reflects
better the imprecision of input data.
Fuzzy knowledge-based modelling can be particularly useful where there is no
analytical model of the relations to be examined or where there is an insufficient
amount of data for statistical analysis, or where the degree of uncertainty of these
data is very high (Salski 1992; Salski et al. 1996; Li 1996; Daunicht et al. 1996;
Bardossy and Duckstein 1995; Pedrycz 1996; Bock and Salski 1998). In these
cases the only basis for modelling is the expert knowledge, which is often
uncertain and imprecise.
1.3
Fuzzy Classification: A Fuzzy Clustering Approach
Conventional clustering methods definitely place an object within only one
cluster. With fuzzy clustering this is no longer essential, since the membership
value of this object can be split up between different clusters. In comparison to
conventional clustering methods the distribution of the membership values
provides additional information - the membership values of a particular object can
be interpreted as the degree of similarity between this object and the respective
clusters (Salski and Kandzia 1996).
Classifying existing chemicals according to their ecotoxicological properties
(Friederichs et al. 1996) can be taken as an application example of the fuzzy
cluster analysis. The large number of existing chemicals makes it necessary to
select representative chemicals which reflect the relevant properties of possibly a
major group of compounds. Therefore the main tasks of this application are:
- to find distinguishable clusters with characteristic properties,
- to find chemicals representative for each cluster,
- to examine the role of different parameters for clustering.
Compared to conventional clustering methods the fuzzy clustering technique is
more appropriate to handle the uncertainty of ecotoxicological data, which results,
for example, from the difficult comparability of these data. The analysis of the
partition efficiency indicators was used to choose the fuzzifier value and the
determination of the optimal number of clusters, e.g.:
- partition entropy (should be minimal),
- partition coefficient, where values closer to I indicate the "better" partition,
- non-fuzziness index, indicating the "best" partition by the highest value,
independently of the number of clusters.