Introduction

Boris Faybishenko1, Rehan Sadiq2, and Ashok Deshpande3

1Lawrence Berkeley National Laboratory, Earth and Environmental Sciences Area, Energy Geosciences Division, Berkeley, California, USA
2School of Engineering, University of British Columbia (Okanagan), Kelowna, BC, Canada
3Berkeley Initiative in Soft Computing (BISC), Special Interest Group Environmental Management Systems (EMS), University of California, Berkeley, California, USA; and College of Engineering, Pune, India

Environmental pollution has been the greatest problem facing humanity for many years, and it is the leading cause of morbidity and mortality. Humankind's activities, such as urbanization, industrialization, mining, exploration, and organic and radioactive contamination, are major reasons of global environmental pollution in both developed and developing nations [e.g. 1, 2]. These problems call for immediate action on initiating pollution abatement strategies. However, predictions and environmental decision-making are often limited due to the uncertainty, vagueness, or ambiguity of observational data [e.g. 3-7]. The methods of statistical mechanics have embraced two-valued logic-based probability theory, wherein a random variable is used as the basis of probability computations. However, the standard probability theory is not designed to deal with imprecise probabilities that pervade real-world uncertainties. Fuzzy set theory is an alternative approach to modeling these uncertainties.

Since the publication of the first scientific paper on fuzzy sets by Lotfi A. Zadeh [8], fuzzy systems modeling has been applied successfully in many scientific and technological fields and has proven useful when dealing with environmental problems. The theory of fuzzy sets is based on the notion of relative graded membership, as inspired by the processes of human perception and cognition. Fuzzy logic (FL) can deal with information arising from computational perception and cognition that is uncertain, imprecise, vague, partially true, or without sharp boundaries. FL allows for the inclusion of vague human assessments in computing problems. Also, it provides an effective means for conflict resolution of multiple criteria and for the better assessment of options [4, 9, 10].

The main idea of the application of FL is the presentation of all system parameters and variables as a matter of degree or partial belief, which will allow one to produce acceptable, definitive outputs in response to incomplete, ambiguous, distorted, or imprecise inputs. Despite FL being successfully applied in various sectors, new applications are constantly being found for FL methods and fuzzy sets.

It is a deep-seated tradition in science to employ the conceptual structure of bivalent logic and probability theory as a basis for the formulation of concepts. What is widely unrecognized is that, in reality, most concepts are fuzzy in nature rather than bivalent, and thus it is generally not possible to accurately formulate most real-world problems within the conceptual structure of bivalent logic and probability theory. Thus, the techniques based on FL are more applicable for environmental system modeling wherein an expert's perception takes center stage of the modeling process.

The fuzzy set of a concept is defined by a distribution function of the degree of belief (DoB) in a qualitative parameter (the concept) over a range of variations in a quantitative or less-qualitative parameter (the scale). The concept may be determined by different scaling parameters, and each parameter on its own is not necessarily unique. So, the form of a fuzzy set depends almost entirely on the scale selected. In the environmental field, regulators, health authorities, epidemiologists, politicians, environmentalists, engineers, and the general public often define a concept, such as contamination, in different ways. The only term which is more or less unequivocally understood by all interested groups is the final risk often associated with dollar value. The proper definition and scaling of fuzzy sets can provide a common language through which experts from different disciplines can communicate during the entire process of risk assessment. Uncertainty in the input information propagates (but is neither magnified nor dampened) in a fuzzy way, so that the output remains fuzzy and can then be translated into either quantitative risk values or qualitative linguistic expressions. In this book, we examine a real risk assessment case scenario using fuzzy arithmetic.

There are several emerging and complex environmental issues wherein fuzzy sets and FL can be applied. FL-based techniques are well suited for problem-solving in a number of environmental study areas, including but not limited to climate change adaptation, water resources management, air quality management, watershed management, wildlife management, flood control and management, water quality management, environmental risk assessment, wildfire control and management, emerging pollutants control, and socioenvironmental issues. The complex environmental issues in these areas can be approached, analyzed, managed, and resolved effectively using FL-based methods. The developed methods are able to measure, evaluate, and analyze complex issues characterized by uncertain, imprecise, ambiguous, and subjective features.

It is important to note that life cycle assessment (LCA) and environmental impact assessment (EIA) are commonly used for evaluating environmental impacts. LCA is used to quantify environmental impacts throughout a product's, system's, or service's entire life. It has also become a measure for evaluating the environmental performance of management strategies and industrial products. Similarly, EIA is applied to evaluate the environmental impacts of any development project before it is implemented, such as a road construction project. Both tools involve extensive modeling. Environmental modeling using imprecise or vague data may consequently lead to inaccurate or uncertain predictions. Expert knowledge is often used to address the issue of a lack of quantitative data. However, expert knowledge is intrinsically associated with uncertainties due to the vagueness and ambiguity of human thoughts. FL can be used to reduce such uncertainties. The modeling of environmental systems is primarily conducted using the principles of either Newtonian mechanics based on closed form solutions with very little uncertainty or statistical methods, such as various optimization techniques, which are based on bivalent probability theory. Moreover, quantitative environmental data can be converted to fuzzy data using fuzzy inference systems (FIS). The hybrid methodology combining FL and LCA or EIA can be used to reduce data-related uncertainty in EIA.

In today's world, data are being generated at an unprecedented speed. This will continue to increase, too. The use of data-driven methods - such as machine learning, artificial intelligence (e.g. artificial neural networks), data mining, case-based reasoning, pattern recognition - is becoming prevalent in systematic decision-making, especially in making "smart" decisions. Such decision-making systems often use automated data collection using sensors and employ the Internet of Things (IoT) for rapid decision-making. The accuracy of such data-driven methods can be improved by incorporating expert knowledge and other qualitative data, and fuzzy set theory and FL can be a powerful enhancement to the intelligent models [11]. The complexity, vagueness, and ambiguity in data can be properly approximated using fuzzy concepts. For example, an adaptive neurofuzzy inference system (ANFIS) integrates both neural networks and the fuzzy inference concept, which can capture the benefits of both techniques. The FIS of ANFIS uses a group of if-then rules that have the capability to approximate highly nonlinear and complex relationships that are indiscernible by conventional mathematical techniques. FL principles enable the intelligent/smart models to conduct approximate reasoning like human brains.

The IoT assists in rapid and automated decision-making even in real time using sensor-generated data transmitted via the Internet. The biggest challenge in such a situation is data reliability. Sensors often generate faulty data, which may adversely affect the accuracy of modeling outcomes. However, the outliers flagged based on the conventional definition of an outlier can be correct data points in a highly complex and irregular system. On the other hand, the data points within a conventional data range can be faulty, too, due to instrumental error. In such situations, FL principles incorporating expert knowledge can be very useful in identifying faulty data. The fuzzy if-then rules are very practical and easier to comprehend and use. Moreover, the use of fuzzy concepts in neural networks reduces computational complexity, which further reduces the computational time in modeling complex systems. The FL-enhanced neural networks also require less cloud space for data storage, ultimately enhancing the efficacy of the developed models and decision-making systems. FL theory and methods can benefit the application of neural networks and data mining techniques. For example, Talpur et al. [12] provide a review of deep neural networks (DNNs) and reasoning aptitude from FIS. This study revealed that the proposed deep neural fuzzy systems' (DNFS) architectures performed better than nonfuzzy models, with an overall accuracy of 81.4%. The novel hybridization of DNN and FL was...