7.1
%XYou and a friend walk outside on an April morning. You announce that the weather is "mild". Your friend declares it "cold". Who is wrong? Or are you both right? We all recognize that language can be imprecise and that words such as cold, hot, or mild do not have well-defined boundaries. In 1965, Lotfi Zadeh introduced fuzzy logic as a means of processing data by extending classical set theory to handle partial membership1. Classical set theory deals with sets that are "crisp" in the sense that members are either in or out according to rules of binary logic. For example the apple in the basket is Red OR Not Red (binary logic). Some of the apples could be categorized as Red AND Not Red (fuzzy logic). Many of the concepts that we deal with in everyday life and in fields such environmental health involve factors that defy classification into "crisp" sets-safe, harmful, acceptable, unacceptable, etc. A classic example is when a regulator, who after she carefully explains the result of a detailed quantitative risk assessment to a community group is then asked "But are we safe?" In this case, "safe," defies crisp classification because it is a multivariate state with gradations, that vary among different individuals and groups.Fuzzy logic has become a common way of dealing with information in a number of fields, such as control theory, smart machines, investment analysis and so on. But the application of fuzzy sets can and has been extended to environmental science and policy. For anyone who has worked on health and environmental issues, it becomes immediately obvious that we deal constantly with fuzzy concepts-hazard, acceptable, safe, etc. Even concepts such as carcinogen and neurotoxin define fuzzy sets whose members are selected by experts who review and make judgments on conflicting toxicology or epidemiology. In spite of their relevance and early efforts to promote their use in risk assessment2, fuzzy logic applications are still rare in risk assessment or other environmental assessments.In this paper we consider whether and how fuzzy logic and fuzzy arithmetic apply to risk assessment and environmental policy. We use a case study assessment of water quality in the Ganga river of India to illustrate this evaluation. Our goal is to consider whether and how much this approach can be applied more broadly for environmental assessments.