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 Strong
	and ‘Threatened Plants’ is Medium
	and ‘Threatened Fishes’ is Weak
	and ‘Threatened Reptiles’ is Strong
	and ‘Threatened	Amphibians’ is Strong
then
  	PR(BIOD) is Bad.

Assessing OSUS from its primary components:

if
	ECOS is Bad
	and HUMS 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.