Fuzzy synthetic evaluation of disinfection by-products—a risk-based indexing system

Abstract

Disinfection by-products (DBPs) are formed when disinfectants such as chlorine, chloramine, and ozone react with organic matter in water. Chlorine being the most common disinfectant used in the drinking water industry worldwide, significant attention has been focused on chlorinated DBPs. A new indexing method using fuzzy synthetic evaluation is proposed to determine the health risk associated with the two major groups of chlorinated DBPs—trihalomethanes (THMs) and haloacetic acids (HAAs). Initially, membership functions for cancer and non-cancer risks associated with THMs and HAAs are used to establish the fuzzy evaluation matrices. Subsequently, weighted evaluation matrices for both types of risks are established by performing cross products on the weighted vectors (founded on the analytic hierarchy process) and the fuzzy evaluation matrices. In the final stage, the weighted evaluation matrices of cancer and non-cancer risks are aggregated to determine the final risk rating. Two case studies are provided to demonstrate the application of this method.

Introduction

Disinfection is performed to eradicate and/or inactivate the pathogens from drinking water. It involves destruction of organization of cell structure, and interference with energy yielding metabolisms, biosynthesis and growth of microbes. Chlorine and its compounds are the most commonly used disinfectants for water treatment. Chlorine has a very strong oxidizing potential, which provides a residual throughout the distribution system and protects against microbial recontamination.

The addition of disinfecting chemicals to drinking water can reduce the microbial risk but poses chemical risk due to the formation of disinfection by-products (DBPs). Formation of DBPs occurs when the disinfectant reacts with natural organic matter and/or inorganic substances present in water. More than 600 DBPs have been identified in laboratory scale studies for different disinfectants, while approximately 250 have been identified in drinking water samples taken from full-scale distribution systems. Among DBPs found in chlorinated drinking water, trihalomethanes (THMs) and haloacetic acids (HAAs) have been the focus of particular attention because of the potential carcinogenicity and harmful non-cancer effects. THMs include four compounds—chloroform (TCM), dichlorobromomethane (DCBM), dibromochloromethane (DBCM) and bromoform (TBM). In waters with low bromide levels, TCM is a major culprit among THMs. HAAs include nine compounds but the most common are—monochloroacetic acid (MCAA), dichloroacetic acid (DCAA), trichloroacetic acid (TCAA), monobromoacetic acid (MBAA), dibromoacetic acid (DBAA), and bromochloroacetic acid (BCAA) (Serodes et al., 2003, Berradi). Among them, generally DCAA and TCAA are of significant levels in chlorinated drinking water.

The major objective of this research is to develop a risk-based indexing system for chlorinated DBPs found in drinking water using the fuzzy synthetic evaluation (FSE) technique. The paper addresses three major issues: identifying toxicity criteria for DBPs, developing an indexing system by grouping DBPs based on associated adverse health effects, and demonstrating the application of this method using two case studies.

The Safe Drinking Water Act requires the United States Environmental Protection Agency (US EPA) to develop new drinking water regulations. The regulations related to DBPs are part of the Microbial-Disinfection by-products (M-DBPs) rule (US EPA, 1999). The DBP regulations are based on evidence of their potential adverse human health effects, in particular cancer and reproductive disorders (Cantor et al., 1998, Graves et al., 2002). Routine water quality sampling helps in identifying whether regulatory thresholds (guideline or standard) of DBPs are violated or not. The threshold values are based on potential toxicity of DBP indicators. A wealth of literature reporting adverse health effects through toxicological laboratory studies is available. Some of the adverse health effects of THMs and few HAAs are summarised in Table 1.

The World Health Organization (WHO, 1993) published drinking water guidelines for a few common DBPs including THMs and HAAs. In addition to guidelines for THMs, the WHO has also suggested that the sum of the ratios of the THM levels to the guideline values should not exceed 1 (see Table 2). Such guidelines have no official recognition in the US or Canada. The US EPA (2001) has established the maximum allowable contaminant level of 0.08 mg/l for total THMs and of 0.06 mg/l for HAA₅ (the sum of five HAAs, that is mono-, di-, and trichloroacetic acids and mono- and dibromoacetic acids), respectively. Compliance is based on an annual running average of quarterly samples, and since 2002 has also been based on a locational running average (Sharfenaker, 2001). Health Canada (2001) has set a total THM level of 0.10 mg/l as an interim maximum acceptable concentration, which serves as a guideline for Provincial regulations. No Canadian drinking water quality guideline exists for other DBPs for the time being. The Aus-NZ, 2000, United Kingdom, 2000 drinking water standards are also summarized in Table 2 for comparison.

Water quality is generally defined by upper and lower limits on selected possible contaminants in water (Maier, 1999). Traditionally, water quality indicators (or parameters) can be grouped into three broad categories—physical, chemical and biological, and each category contains a number of water quality variables. The acceptability of water quality for its intended use depends on the magnitude of these indicators (Swamee and Tyagi, 2000), and is often governed by regulations. A water quality failure is often defined as an exceedence of one or more water quality indicators (DBPs) from specific regulations, or in the absence of regulations, exceedence of guidelines or self-imposed, customer-driven limits.

Recently, a significant amount of literature has been published on describing the overall (aggregate) water quality by an index using various statistical and mathematical techniques. Swamee and Tyagi (2000) have discussed in detail the pros and cons of different techniques and approaches available for evaluating the water quality index. Sinha et al. (1994) combined pH, chloride concentration, turbidity, residual chlorine, conductivity and MPN (most probable number—a bacterial counting technique) into a single water quality index through a weighting scheme, which can represent overall water quality at various nodes in the distribution system. The normalized water quality index (0–100) defines the overall water quality in each segment of the distribution system.

Sadiq et al., 2003, Sadiq et al., 2004a have recently suggested a fuzzy-based framework for the analysis of aggregative risk associated with water quality failure in distribution systems. The basic risk items are grouped into higher level risk factors, to form a multi-stage hierarchical model of aggregative risk for water quality failure in the distribution network. The usage of fuzzy set techniques for water quality indexing enables the incorporation of hard field data (e.g. observed water quality) and soft qualitative data (e.g. expert opinion).

The term soft computing describes an array of emerging techniques such as fuzzy logic, probabilistic reasoning, neural networks, and genetic algorithms. All these techniques are essentially heuristic and provide rational and reasoned out solutions for complex real-world problems (Bonissone, 1997). Quantitative aggregation of risk due to multiple sources is a complex process, which warrants soft computing techniques.

Fuzzy logic provides a language with syntax and semantics to translate qualitative knowledge into numerical reasoning. In many engineering problems, the information about the probabilities of various risk items is vaguely known or assessed. The term computing with words has been introduced by Zadeh (1996) to explain the notion of reasoning linguistically rather than with numerical quantities. Such reasoning has a central importance for many emerging technologies related to engineering and applied sciences. This approach has proved very useful in medical diagnosis (Lascio et al., 2002), information technology (Lee, 1996), water quality assessment (Lu et al., 1999, Lu and Lo, 2002), corrosion of cast iron pipes (Sadiq et al., 2004b) and in many other industrial applications (Lawry, 2001).

When evaluating risk items in complex systems, decision-makers, engineers, managers, regulators and other stake-holders often view risk in terms of linguistic variables like very high, high, very low, low, etc. The fuzzy set theory is able to deal effectively with uncertain, vague and linguistic variables, which can be used for approximate reasoning and subsequently manipulated to propagate the uncertainties throughout the decision process. Fuzzy-based techniques are a generalized form of interval analysis used to address uncertain and/or imprecise information. A fuzzy set describes the relationship between an uncertain quantity x and a membership function μ, which ranges between 0 and 1. A fuzzy set is an extension of the traditional set theory (in which x is either a member of set A or not) in that an x can be a member of set A with a certain degree of membership μ. To qualify as a fuzzy number, a fuzzy set must be normal, convex and bounded (see Klir and Yuan, 1995 for definitions of these terminologies). Any shape of a fuzzy number is possible, but the selected shape should be justified by available information. Generally, triangular fuzzy numbers (TFNs) or trapezoidal fuzzy numbers (ZFN) are used for representing linguistic variables (Lee, 1996). Defuzzification is a process to evaluate a crisp or point estimate of a fuzzy number. A defuzzified value is generally represented by the centroid, often determined using the centre of area method (Yager, 1980).

Fuzzy-based techniques can help in addressing deficiencies inherent in binary logic and are useful in propagating uncertainties through models. Contrary to binary logic, fuzzy-based techniques can provide an intensity of exceeding regulated thresholds with the help of memberships to various risk levels. In water quality modeling, the fuzzy set theory has been used for classification of rivers since 1980s. The majority of research has been focused on fuzzy synthetic evaluation (FSE) and fuzzy clustering analysis (FCA). The FSE is used to classify samples at a known centre of classification (or group), whereas the FCA is used to classify samples according to their relationships when this centre is unknown (Lu et al., 1999). The FSE classifies samples for known standards and guidelines, and is a modified version of traditional synthetic evaluation techniques.