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Nonlinearity, fuzziness and incommensurability in indicator-based assessments of vulnerability to climate change: A new mathematical framework

El-Zein, Abbas, Tonmoy, Fahim N
Ecological indicators 2017 v.82 pp. 82-93
climate, climate change, decision making, heat, models, mortality, risk assessment, temperature, uncertainty, utility functions
The earth’s climate system is highly nonlinear and the vulnerability of a community to a climate hazard is no exception. While this fact is widely accepted, indicator-based vulnerability assessments (IBVA) hardly ever take such nonlinearities into account. This is mainly due to the fact that the majority of assessment studies use methods based on Multiple Attribute Utility Theory (MAUT) (e.g. simple additive weight or multiplicative aggregation) to aggregate indicators. These methods convert all indicators into a global utility function and produce only a linear, threshold-free scaling of the effects of an indicator on vulnerability. In a previous paper, we showed that outranking procedures developed in decision-making science offer a more theoretically-sound approach to aggregation because they allow the analyst to incorporate the incommensurability, fuzziness and uncertainty associated with indicators. In this paper, we develop a new mathematical framework for vulnerability in order to clearly identify various sources of nonlinearity and incommensurability in vulnerability assessments. We then propose a new outranking formulation which can accommodate both and can be used to conduct assessments at different scales. We do so by introducing the concept of harm criterion as a mediator between an indicator and the vulnerability it represents. The new assessment approach can aggregate a mix of indicators with various degrees of subjectivity and non-linearity, without converting them into a single utility function and without requiring them to be mutually compensating.We illustrate the proposed approach by applying it to a simplified model of urban vulnerability to heat, focusing on the non-linear relationship between mortality and temperature above a ‘comfort temperature’, long evidenced in the epidemiological literature. We compare vulnerability rankings yielded by linear and non-linear characterizations of the relationship between temperature and mortality and find that the incorporation of non-linearity can have a significant impact on the rankings.