15.4 Applications of the Fuzzy Modeling Approach to Ecological Assessment
217
adaptive hierarchical fuzzy c-means clustering algorithm and its generalization (e.g., the ISODATA
methods). We can use multitier data, quantitative
or qualitative.
15.4.2 Adaptive Fuzzy
Modeling Approach
An adaptive fuzzy system is a fuzzy logic system
equipped with a training algorithm, where the fuzzy
logic system is constructed from a collection of
fuzzy IF-THEN rules, and the training algorithm
adjusts the parameters of the fuzzy logic system
based on numerical input-output pairs. Conceptually, adaptive fuzzy systems combine linguistic and
numerical information in the following way. Because fuzzy logic systems are constructed from
fuzzy IF-THEN rules, linguistic information in the
form of fuzzy IF-THEN rules can be directly incorporated; on the other hand, numerical information in the form of input-output pairs is incorporated by training the fuzzy logic system to match
the input-output pairs. Adaptive fuzzy systems can
be viewed as fuzzy logic systems whose rules are
automatically generated through training. There are
two strategies for combining numerical and linguistic information by using adaptive fuzzy systems:
1. Use linguistic information to construct an initial
fuzzy logic system, and then adjust the parameters of the initial fuzzy-Iogic-system-based numerical information. The final fuzzy logic system is, therefore, constructed based on both
numerical and linguistic information.
2. Use numerical information and linguistic information to construct two separate fuzzy logic systems, and then use a fuzzy weighted average to
obtain the final fuzzy logic system.
Many training methods have been proposed in
the fuzzy research community, including backpropagation, orthogonal least squares, a tablelookup scheme, nearest-neighborhood clustering,
and evolutionary learning. Among them, neurofuzzy data analysis has gained great attention recently (Ichihashi and Turksen, 1995).
Li and Yeung (1994) have considered using an
adaptive fuzzy data modeling framework for characterization of subsurface contamination. Similarly, this approach can be used in data analysis in
ecological assessment. Characterizing a contaminated subsurface involves a complex interaction between subsurface contaminants and the soil-water
system. The composition and properties of contaminants are significant factors in the development of
such interaction relationships. However, basic
chemical-physical data, the concentration data, and
the toxicological data are often unavailable. The
existence of a large number of subsurface sites suspected of being contaminated requires us to obtain
a relative estimation among these sites with respect
to their hazard potential. We use the relative estimation of hazard as a basis for deciding about the
urgency of carrying out a remedial measure.
We have developed an adaptive fuzzy modeling
framework as a new approach to the characterization of subsurface on the basis of consideration of
the relative estimation of hazard. This system involves several different data analysis methods (Figure 15.2), including a pure fuzzy logic system (IFTHEN rules) and fuzzy classification linking a
training (or learning) algorithm (back-propagation
algorithm) that have been developed recently in the
fuzzy research community; for example, see Wang
(1994). This system combines linguistic and numerical information from expert knowledge and
field sampling data. In data preprocessing and algorithmic data analysis, we use traditional statistiDa ta P reproce ssing
Data
Experts
Algorithmic
Data Analysis
IF-THEN Based
Data Analysis
Neuro-fuzzy
Data Analysis
FIGURE 15.2. The procedure of data analysis in an adaptive fuzzy modeling framework for characterizing potentially
subsurface contaminants (modified from Li and Yeung, 1994).
217
adaptive hierarchical fuzzy c-means clustering algorithm and its generalization (e.g., the ISODATA
methods). We can use multitier data, quantitative
or qualitative.
15.4.2 Adaptive Fuzzy
Modeling Approach
An adaptive fuzzy system is a fuzzy logic system
equipped with a training algorithm, where the fuzzy
logic system is constructed from a collection of
fuzzy IF-THEN rules, and the training algorithm
adjusts the parameters of the fuzzy logic system
based on numerical input-output pairs. Conceptually, adaptive fuzzy systems combine linguistic and
numerical information in the following way. Because fuzzy logic systems are constructed from
fuzzy IF-THEN rules, linguistic information in the
form of fuzzy IF-THEN rules can be directly incorporated; on the other hand, numerical information in the form of input-output pairs is incorporated by training the fuzzy logic system to match
the input-output pairs. Adaptive fuzzy systems can
be viewed as fuzzy logic systems whose rules are
automatically generated through training. There are
two strategies for combining numerical and linguistic information by using adaptive fuzzy systems:
1. Use linguistic information to construct an initial
fuzzy logic system, and then adjust the parameters of the initial fuzzy-Iogic-system-based numerical information. The final fuzzy logic system is, therefore, constructed based on both
numerical and linguistic information.
2. Use numerical information and linguistic information to construct two separate fuzzy logic systems, and then use a fuzzy weighted average to
obtain the final fuzzy logic system.
Many training methods have been proposed in
the fuzzy research community, including backpropagation, orthogonal least squares, a tablelookup scheme, nearest-neighborhood clustering,
and evolutionary learning. Among them, neurofuzzy data analysis has gained great attention recently (Ichihashi and Turksen, 1995).
Li and Yeung (1994) have considered using an
adaptive fuzzy data modeling framework for characterization of subsurface contamination. Similarly, this approach can be used in data analysis in
ecological assessment. Characterizing a contaminated subsurface involves a complex interaction between subsurface contaminants and the soil-water
system. The composition and properties of contaminants are significant factors in the development of
such interaction relationships. However, basic
chemical-physical data, the concentration data, and
the toxicological data are often unavailable. The
existence of a large number of subsurface sites suspected of being contaminated requires us to obtain
a relative estimation among these sites with respect
to their hazard potential. We use the relative estimation of hazard as a basis for deciding about the
urgency of carrying out a remedial measure.
We have developed an adaptive fuzzy modeling
framework as a new approach to the characterization of subsurface on the basis of consideration of
the relative estimation of hazard. This system involves several different data analysis methods (Figure 15.2), including a pure fuzzy logic system (IFTHEN rules) and fuzzy classification linking a
training (or learning) algorithm (back-propagation
algorithm) that have been developed recently in the
fuzzy research community; for example, see Wang
(1994). This system combines linguistic and numerical information from expert knowledge and
field sampling data. In data preprocessing and algorithmic data analysis, we use traditional statistiDa ta P reproce ssing
Data
Experts
Algorithmic
Data Analysis
IF-THEN Based
Data Analysis
Neuro-fuzzy
Data Analysis
FIGURE 15.2. The procedure of data analysis in an adaptive fuzzy modeling framework for characterizing potentially
subsurface contaminants (modified from Li and Yeung, 1994).