4
A. Salski
There are a lot of good books containing details about fuzzy sets and fuzzy
logic such as Zimmermann (1993), Kruse et al. (1995), Bardossy and Duckstein
(1995) and Pedrycz (1996).
1.2
Fuzzy Approach to Ecological Modelling and Data
Analysis
Heterogeneity and uncertainty belong to the characteristic properties of the data
stored in ecological data bases and ecological information systems. Ecologists
collect and use information from various heterogeneous data and knowledge
sources - sources of objective (mostly quantitative) information, e.g. measurement
and calculation, and sources of subjective (often only qualitative) information, e.g.
expert knowledge and subjective evaluations instead of measurement data.
Therefore in many fields of ecological research ecologists have to work with a
necessarily subjective mixture of quantitative and qualitative information. Not all
ecological parameters are measurable (for example the number of fish in a
particular lake); the values of such parameters can be obtained by special
estimation or evaluation methods, which are often of a subjective character.
Ecological data can also have different structures and formats (e.g. time series and
spatial data).
The problem of uncertainty often appears in ecological modelling, in particular
it concerns the uncertainty of data and vaguely defined expert knowledge. A large
inherent uncertainty of ecological data results from the presence of random
variables, incomplete or inaccurate data, approximate estimations instead of
measurements (due to technicalor financial problems) or incomparability of data
(resulting from varying measurement or observation conditions). There are a
number of ways to deal with uncertainty problems, e.g. probabilistic inference
networks (Pearl 1988) or belief intervals (Shafer et al. 1990). One of the most
successful methods of dealing with uncertainty is the fuzzy approach. Fuzzy
approach does not mean a particular method but the integration of a fuzzy concept
into conventional methods of knowledge processing and data analysis. That
means an extension of conventional methods, which is capable of utilising
imprecise, heterogeneous and uncertain data. Compared to conventional methods
the fuzzy approach enables us to make better use of imprecise ecological data and
vague expert knowledge in two ways:
- the representation and handling of imprecise data defined as fuzzy sets,
- the representation and processing of vague knowledge in the form of
linguistic rules with imprecise terms defined as fuzzy sets.
Ecological data or classes of ecological objects can be defined as fuzzy sets with
no sharply defined boundaries, which reflects better the continuous character of
nature. Fuzzy sets can be used to handle uncertainty of data and fuzzy logic to
handle inexact reasoning. Fuzzy logic allows working with uncertain knowledge
about relations between ecosystem components and building models based on this
type of information.
A. Salski
There are a lot of good books containing details about fuzzy sets and fuzzy
logic such as Zimmermann (1993), Kruse et al. (1995), Bardossy and Duckstein
(1995) and Pedrycz (1996).
1.2
Fuzzy Approach to Ecological Modelling and Data
Analysis
Heterogeneity and uncertainty belong to the characteristic properties of the data
stored in ecological data bases and ecological information systems. Ecologists
collect and use information from various heterogeneous data and knowledge
sources - sources of objective (mostly quantitative) information, e.g. measurement
and calculation, and sources of subjective (often only qualitative) information, e.g.
expert knowledge and subjective evaluations instead of measurement data.
Therefore in many fields of ecological research ecologists have to work with a
necessarily subjective mixture of quantitative and qualitative information. Not all
ecological parameters are measurable (for example the number of fish in a
particular lake); the values of such parameters can be obtained by special
estimation or evaluation methods, which are often of a subjective character.
Ecological data can also have different structures and formats (e.g. time series and
spatial data).
The problem of uncertainty often appears in ecological modelling, in particular
it concerns the uncertainty of data and vaguely defined expert knowledge. A large
inherent uncertainty of ecological data results from the presence of random
variables, incomplete or inaccurate data, approximate estimations instead of
measurements (due to technicalor financial problems) or incomparability of data
(resulting from varying measurement or observation conditions). There are a
number of ways to deal with uncertainty problems, e.g. probabilistic inference
networks (Pearl 1988) or belief intervals (Shafer et al. 1990). One of the most
successful methods of dealing with uncertainty is the fuzzy approach. Fuzzy
approach does not mean a particular method but the integration of a fuzzy concept
into conventional methods of knowledge processing and data analysis. That
means an extension of conventional methods, which is capable of utilising
imprecise, heterogeneous and uncertain data. Compared to conventional methods
the fuzzy approach enables us to make better use of imprecise ecological data and
vague expert knowledge in two ways:
- the representation and handling of imprecise data defined as fuzzy sets,
- the representation and processing of vague knowledge in the form of
linguistic rules with imprecise terms defined as fuzzy sets.
Ecological data or classes of ecological objects can be defined as fuzzy sets with
no sharply defined boundaries, which reflects better the continuous character of
nature. Fuzzy sets can be used to handle uncertainty of data and fuzzy logic to
handle inexact reasoning. Fuzzy logic allows working with uncertain knowledge
about relations between ecosystem components and building models based on this
type of information.