## Fuzzy assessment

Sustainable decision-making involves complex, often ill-defined parameters with a high degree of uncertainty due to incomplete understanding of the underlying issues. The dynamics of any socio-environmental system cannot be described by traditional mathematics because of its inherent complexity and ambiguity. In addition, the concept of sustainability is polymorphous and fraught with subjectivity. It is therefore more appropriate to use fuzzy logic for its assessment.

Fuzzy logic is a scientific tool that permits modeling a system without detailed mathematical descriptions, using qualitative as well as quantitative data. The SAFE model uses fuzzy logic to compute composite indicators (outputs) from basic ones (inputs). The computations are done with words using knowledge that is represented by linguistic rules of the form

if (inputs) then (outputs).

Below we give two examples of such “if-then” rules, which are used in the first and last stages of the SAFE inference process.

Assessing a tertiary variable from basic indicators:

if ‘Threatened Mammals’ is Medium ‘Threatened Birds’ is Strongand‘Threatened Plants’ is Mediumand‘Threatened Fishes’ is Weakand‘Threatened Reptiles’ is Strong and ‘Threatened Amphibians’ is Strong then PR(BIOD) is Bad.

Assessing OSUS from its primary components:

if ECOS is BadandHUMS is Good then OSUS is Intermediate.

The terms Medium, Bad, Intermediate, etc. in the rules given above represent
fuzzy sets. Each rule has a given degree of truth or *firing strength*,
which is an aggregate measure of the degree to which its inputs belong to
the corresponding fuzzy sets. The method we describe next, called *fuzzification*,
is used to compute the degree to which a basic indicator belongs to a specific
fuzzy set.