Fuzzy indices of environmental conditions
Section snippets
Fuzzy memberships as environmental indices
Environmental indices rarely have much significance by themselves. Knowing that some variable like pollutant concentration or soil acidity has a specific value is usually meaningful only in the context of knowledge of natural background levels, regulatory policy, and the vulnerability of key environmental components. For this reason it is useful, and probably more practical, to relate these indices to some sort of acceptability measure, which can be interpreted as the membership in a fuzzy set
Mathematical formalism
Traditionally the symbol μ has been used to represent fuzzy memberships. If x represents the value of an environmental variable, then μ(x) is the corresponding membership in the set of acceptable conditions, and takes a value between zero and one. For example, if a lake becomes hypoxic and all the fish die, then μ would presumably be zero, indicating that this situation is totally unacceptable.
In most situations more than one environmental variable is important, and we can define μi(xi), which
Examples
Several applications of this approach have been implemented, or are under consideration. Two are described below, one of which is very specific and has been worked out in detail, the other of which is more general and addresses issues which have not yet been fully resolved.
Combining fuzzy indices
One aspect of the problem of applying fuzzy indices to complex situations is the need to combine different indices representing different impacts. Perhaps the strongest positive feature of fuzzy logic in developing environmental indices is the ability to combine such indices much more flexibly than one can combine discrete measures, which are often simply binary indices corresponding to ordinary (‘crisp’) sets, such as ‘acceptable versus unacceptable’. For this reason it is important to discuss
Multi-objective decision making
As pointed out earlier, society is not always able to reach consensus on the value of certain components of the environment, so that effects which are acceptable to some segments may be far less acceptable to others. Examples include the abundances of certain birds and marine mammals, which are highly prized for their beauty and entertainment value by recreational users of the environment, but are seen as predators and competitors by fishers and farmers. Many complex issues deal with the
Consensus building with fuzzy logic
Multi-objective decision making is at the heart of the political process, which involves trying to build a consensus among groups with different values and goals. The formalism described above can be used to identify key areas of disagreement and may possibly contribute to the resolution of conflict in complex situations by providing a language for quantifying these disagreements.
I propose a three-step procedure to deal with these kinds of disagreements:
- 1.
Identify environmental variables on which
Conclusion
Fuzzy logic can be applied to the development of environmental indices in a way that resolves many common problems, such as incompatible observations and implicit value judgements. It bridges the gap between scientific measurement and the fulfilment of social objectives and provides a way to translate a wide variety of information — objective data, qualitative information, subjective opinions, and social needs — into a common language for characterising environmental effects.
Because it offers a
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