Chapter 1 . Applications of Fuzzy Logic
5
Ecological modelling and data analysis are the main application areas of the
fuzzy set theory in ecological research. The integration of the fuzzy inference
mechanisms and the expert system technique provides development tools for
fuzzy expert systems and fuzzy knowledge-based models of ecological processes
(Salski 1999). The evolution of conventional knowledge-based systems into fuzzy
systems (adding imprecision or uncertainty handling to conventional systems)
makes the extension of their application area for complex ecological problems
possible (Kampichler et al. 2000; Freyer 2000; Zhu et al. 1996; Bock and Salski
1996). There are also other fuzzy approaches to ecological modelling, e.g. the
fuzzy statistical approach to ecological assessments (Li 2001), the fuzzy
differential equations for fuzzy modelling in population dynamics (Barros et al.
2000) or ecological impact analysis using fuzzy logic (Enea et al. 2001; Silvert
1997). The fuzzy memberships can be also used as environmental indices (Silvert
2000) or as a fuzzy association degree in the ecosystem modelling (Liu 2001).
There are also an increasing number of other combined approaches, which result
from linking the fuzzy approach with other techniques, e.g.:
- fuzzy approach with neural networks for assessment in spatial decision making
(Zheng 2001) or for habitat modelling in agricultural landscapes (Wieland et al.
1996),
- fuzzy modelling with conventional dynamic programming to optimal biological
control of a greenhouse mite (Cheng et al. 1996),
- fuzzy approach with linear programming for the optimization of land use
scenarios (Salski et al. 2001),
- fuzzy approach with probabilistic uncertainty to model climate-plant-herbivore
interactions in grassland ecosystems (Wu et al. 1996),
- fuzzy approach with three-dimensional modelling technique (Ameskamp 1997).
The next important research field is handling uncertainty in geographic
information systems, that means dealing with fuzziness in reasoning with spatial
data (Dragicevic 2000; Guesgen 2000) and in the assignment of locations to
cIasses (Burrough 2000; MacMillan 2000) or fuzziness in the definitions of object
boundaries (Cross 2000).
Some application examples of a fuzzy approach to ecological modelling and
data analysis are presented in this paper, namely fuzzy clustering as a tool for
fuzzy classification of ecological data, fuzzy kriging as a method of fuzzy
interpolation of spatial data and fuzzy knowledge-based modelling.
Fuzzy classification and fuzzy geostatistik belong to the main problems of the
analysis of ecological data. Conventional classification methods based on Boolean
logic ignore the continuous nature of ecological parameters and the uncertainty of
data, which can result in misclassification. Fuzzy classification, wh ich means the
division of objects into classes that do not have sharply defined boundaries, can be
carried out in various ways, for example:
- application of fuzzy arithmetical and logical operations, e.g. to determine land
suitability (Burrough et al. 1992),
- fuzzy clustering, e.g. to classify some crop growth parameters (Marsili-Libelli
1994) or to classify existing chemicals according to their ecotoxicological
properties (Friederichs et al. 1996).
5
Ecological modelling and data analysis are the main application areas of the
fuzzy set theory in ecological research. The integration of the fuzzy inference
mechanisms and the expert system technique provides development tools for
fuzzy expert systems and fuzzy knowledge-based models of ecological processes
(Salski 1999). The evolution of conventional knowledge-based systems into fuzzy
systems (adding imprecision or uncertainty handling to conventional systems)
makes the extension of their application area for complex ecological problems
possible (Kampichler et al. 2000; Freyer 2000; Zhu et al. 1996; Bock and Salski
1996). There are also other fuzzy approaches to ecological modelling, e.g. the
fuzzy statistical approach to ecological assessments (Li 2001), the fuzzy
differential equations for fuzzy modelling in population dynamics (Barros et al.
2000) or ecological impact analysis using fuzzy logic (Enea et al. 2001; Silvert
1997). The fuzzy memberships can be also used as environmental indices (Silvert
2000) or as a fuzzy association degree in the ecosystem modelling (Liu 2001).
There are also an increasing number of other combined approaches, which result
from linking the fuzzy approach with other techniques, e.g.:
- fuzzy approach with neural networks for assessment in spatial decision making
(Zheng 2001) or for habitat modelling in agricultural landscapes (Wieland et al.
1996),
- fuzzy modelling with conventional dynamic programming to optimal biological
control of a greenhouse mite (Cheng et al. 1996),
- fuzzy approach with linear programming for the optimization of land use
scenarios (Salski et al. 2001),
- fuzzy approach with probabilistic uncertainty to model climate-plant-herbivore
interactions in grassland ecosystems (Wu et al. 1996),
- fuzzy approach with three-dimensional modelling technique (Ameskamp 1997).
The next important research field is handling uncertainty in geographic
information systems, that means dealing with fuzziness in reasoning with spatial
data (Dragicevic 2000; Guesgen 2000) and in the assignment of locations to
cIasses (Burrough 2000; MacMillan 2000) or fuzziness in the definitions of object
boundaries (Cross 2000).
Some application examples of a fuzzy approach to ecological modelling and
data analysis are presented in this paper, namely fuzzy clustering as a tool for
fuzzy classification of ecological data, fuzzy kriging as a method of fuzzy
interpolation of spatial data and fuzzy knowledge-based modelling.
Fuzzy classification and fuzzy geostatistik belong to the main problems of the
analysis of ecological data. Conventional classification methods based on Boolean
logic ignore the continuous nature of ecological parameters and the uncertainty of
data, which can result in misclassification. Fuzzy classification, wh ich means the
division of objects into classes that do not have sharply defined boundaries, can be
carried out in various ways, for example:
- application of fuzzy arithmetical and logical operations, e.g. to determine land
suitability (Burrough et al. 1992),
- fuzzy clustering, e.g. to classify some crop growth parameters (Marsili-Libelli
1994) or to classify existing chemicals according to their ecotoxicological
properties (Friederichs et al. 1996).