(28d) A Fuzzy Logic Global Optimization Approach to Sustainability Assessment

Fuzzy logic has been used extensively to evaluate the sustainability of an entity based on a number of basic indicators (air, land, economy, health, etc.). Prior models have taken specific values of basic indicator data, created a fuzzy set hierarchy, and computed an exact value for an overall sustainability index of the entity. The latter step required a "defuzzification" process that allowed the exact calculation of that index.

In reality, exact values for basic indicators are either difficult to come by or, even when known, contain significant levels of uncertainty. To address this shortcoming, in this work we propose a novel approach that allows basic indicator data to be provided in the form of intervals which are guaranteed to contain all possible basic indicator values. As a result, all possible values of the overall sustainability index are guaranteed to belong to an interval. This work quantifies the tightest possible interval range for the overall sustainability index, whose computation is achieved through global optimization techniques. Properties of the underlying global optimization problems are first established, and then utilized in the development of an algorithm that exactly quantifies the range of the overall sustainability index, in a finite number of iterations.