A fuzzy logic approach for evaluating ecosystem sustainability

Conventional approaches for assessing the strong sustainability of ecosystems are based on crisp sets for ecosystem attributes or indicators of sustainability, such as regional income, biodiversity and water quality. Defining strong sustainability in terms of crisp sets for attributes presumes the ecosystem manager can make a sharp, unambiguous distinction between an ecosystem that is strongly sustainable and one that is not by comparing measured attributes to sustainability thresholds for those attributes. Making such fine distinctions is incompatible with the uncertainties inherent in ecosystem assessments, and could give rise to faulty or misleading conclusions. An alternative approach for evaluating strong sustainability is proposed that uses fuzzy sets to develop fuzzy propositions about ecosystem attributes and strong sustainability, and applies fuzzy logic to evaluate those propositions. Two kinds of fuzzy propositions are evaluated; unconditional and qualified, and conditional and qualified. While a fuzzy logic approach overcomes the limitation of basing sustainability assessments on crisp sets for the attributes, its implementation requires more information than conventional approaches. In particular, evaluation of unconditional and qualified propositions requires the ecosystem manager to: (1) specify fuzzy sets for all attributes and probability qualifiers; (2) estimate the frequency distribution for ecosystem attributes; and (3) develop a rule for inferring strong sustainability from fuzzy propositions. Evaluation of conditional and qualified propositions requires the ecosystem manager to: (1) specify the prior probability the ecosystem is strongly sustainable; (2) define fuzzy sets for combinations of attribute values and probability qualifiers; (3) estimate the joint frequency distribution for ecosystem attributes; and (4) develop a rule for inferring strong sustainability from fuzzy propositions. An ecosystem manager needs to weigh the advantages of a fuzzy logic approach in terms of overcoming the limitation of conventional approaches against the disadvantage of greater informational requirements.