Fuzzy Assessment

Sustainable decision-making involves complex and often poorly defined parameters with an upper layer of uncertainty due to an incomplete understanding of the underlying problem. The dynamics of social environmental systems cannot be explained with traditional mathematics, taking into account the inherent complexity and ambiguity. Also, the concept of sustainability is polymorphic and full of subjectivity. Therefore, it is getting closer and closer to using fuzzy logic for evaluation.

Fuzzy logic is a scientific tool that allows you to model systems without detailed mathematical explanations using qualitative and quantitative data. The SAFE model uses fuzzy logic to calculate complex indicators (outputs) from critical items (inputs). Calculations are washed into words using knowledge expressed in formal language rules.

( inputs )

then

( outputs )

Two examples of such "IF-THEN" rules, which are used in the first and last stages of the SAFE inference process, are given in the following.

Assessing a tertiary variable from vital indicators:

’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 whilom represent fuzzy sets. Each rule has a given stratum of truth or firing strength, which is a volume measure of the stratum to which its inputs vest to the respective fuzzy sets. The method we describe next, tabbed fuzzification, is used to compute the stratum to which a vital indicator belongs to a specific fuzzy set.

The normalized vital indicators are fuzzified using three fuzzy sets with linguistic values:

• Weak (W)
• Medium (M)
• Strong (S)

For composite indicators (primary, secondary, and tertiary components), five linguistic values are used:

• Very Bad (VB)
• Bad (B)
• Average (A)
• Good (G)
• Very Good (VG)

The overall sustainability is measured using nine fuzzy sets:

• Extremely Low (EL)
• Very Low (VL)
• Low (L)
• Fairly Low (FL)
• Intermediate (I)
• Fairly Upper (FH)
• High(H)
• Very Upper (VH)
• Extremely Upper (EH)

Each indicator value x belongs to one or increasingly fuzzy sets with unre- pealable membership grades. For simplicity, triangular membership functions g(x) are used. For example, in 2002, 13.7% of the mammal species in Greece were endangered. The target value for this indicator is T=t=0%, and the upper threshold of unsustainable values is U=35.5%. The normalized value for this indicator is x=(13.7—35.5)/(0—35.5)=0.614. This value belongs to the fuzzy set Medium with membership grade |дМ(0.614)=0.965 and to the fuzzy set Strong with grade gS(0.614)=0.035.