The fuzzy tool follows the four steps inevitable in a fuzzy process:

1. Determination of suitable assessment parameters (input definition)
   The first step in the fuzzy process is the identification and selection of suitable assessment parameters which describe the indicator with regard to its impact on the environmental quality criterion.
   
   
2. Assignment of membership functions (fuzzification)
   As knowledge usually is uncertain, how the different parameters will precisely affect the indicator in question and to what extent cannot be excactly measured. For the assessment, the numerical values (either on a cardinal or ordinal scale) are translated into “words”, i.e. certain linguistic expressions. This procedure is called fuzzification and is done by assigning so-called membership functions to each input and output parameter.
   
   
3. Rule definition using if-then conditions
   After fuzzification the numerical values of the assessment parameter are no longer used. Instead, the linguistic terms as their ‘fuzzy’ representatives are employed to define rules which describe the interrelations between the assessment parameters in form of if-then-conditions. This step is referred to as “inference” or “fuzzy reasoning”.
   
   
4. Defuzzification of output
   In order to generate a precise result value to interpret the outcome of the assessment a defuzzification method has to be applied. A widely acknowledged defuzzification method is the centre of gravity method. Result of the assessment is a dimensionless ecological index ranging between zero and one.

The fuzzy-logic-based ecological assessment was implemented with the MATLAB Fuzzy Logic Toolbox. For more details the reader can refer to the respective user guide and the MATLAB product webpage:

User guide available at:
http://www.mathworks.com/access/helpdesk/help/pdf_doc/fuzzy/fuzzy.pdf

Webpage:
http://www.mathworks.com/products/fuzzylogic/index.html

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