Fuzzy system modelling of drinking water consumption prediction Zekâi S ßen, Abdüsselam Altunkaynak * _ Istanbul Technical University, Civil Engineering Faculty, Hydraulics Division, Maslak, 34469 _ Istanbul, Turkey article info Keywords: Physical activity Fuzzy model Temperature Uncertainty Water consumption Weight abstract It is important to determine the amount of daily drinking water requirement for a person not only for the health of people but also for the planning and management of the water resources. Physical activity, body weight and temperature play significant role in drinking water consumption rates. Human activity vari- ables are most often given in crisp numerical interval classifications for water consumption calculations. The aim of this paper is to establish a fuzzy model for predicting the water consumption rates based on data at the hand. The fuzzy sets such as low, medium, high can be used to quantify vague, imprecise or incomplete descriptions which are collectively referred to as fuzzy data in the literature. Fuzzy model inputs are considered as the physical activity, body weight and temperature, whereas the output is the water consumption levels. The fuzzy sets are chosen in an appropriate manner and the prediction model of water consumption is compared with the actual consumption amounts. It is not possible to treat such linguistic fuzzy data by statistical methods. It is observed that the model predictions have less than 5% relative error. The model is tested with an independent data set for its successful prediction capability. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Water resources have a great importance for the individuals, societies, countries and humanity, in general. The welfare level of a country is measured with the amount of water consumption per person and quality of the provided water. Although there are many statistical or stochastic methods for modelling water quality or drinking water consumption rates, they are based on crisp inter- val values. Working with crisp intervals may cause loss of informa- tion or miscalculations. However, in fuzzy logic approach it is possible to express crisp intervals in terms of linguistic subsets by fuzzy words such as low, medium, high, good, moderate, poor, etc. Each of these words represents the sub-range of the entire var- iability of the variables concerned (Altunkaynak & S ßen, 2007; Altunkaynak, Özger, & Çakmakci, 2005; Kiska, Gupla, & Nikiforuk, 1985; Kosko, 1987; Mamdani, 1974; Ross, 1995; S ßen, 2001; S ßen & Altunkaynak, 2004; Zadeh, 1965). Both variability and uncertainty in determining the drinking water consumption include several concepts, and the exact defini- tion of these terms varies across the interdisciplines (Reichard, Hauchman, & Soncha, 2000). These concepts depend on issues that distinguish inherent physical or natural characteristics from limi- tations of knowledge or understanding, hence leaving the planner with uncertain, incomplete and vague information, i.e. fuzzy data. The uncertainty aspects in drinking water have already been explained by EPA (1997). Uncertainties are referred to the observed or measurable differences attributable to diversity in a population. For instance, members of population exhibit variability with their weight or physical activity. Imprecision is defined as a degree of uncertainty among an exposed population due to intersubject dif- ferences in distinct conditions such as rates of intake depending on environmental and body temperatures, inhalation rates (physical activity) per unit body mass, uptake fraction, retention characteris- tics, biotransformation and sensitivity (Raucher, Frey, & Cook, 2000). Future water demand depends on consumer preference (or individual unit consumption). However, less attention has been gi- ven to consumer preferences which can be determined by market purchase analysis and varies from place to place with cultural, environmental and other features. In cases of crisp data availabil- ity, regression techniques can be used to relate consumer prefer- ence such as drinking water consumption to specific independent variables. Any regression analysis requires a set of assumptions such as linearity, normality and independence of errors, homosca- dacity which are not achieved most frequently in practice (Benja- min & Cornell, 1970). Furthermore, regression techniques are not capable of digesting linguistic fuzzy data. Especially, drinking water consumption variables are mostly linguistic, and therefore, regression approaches cannot be employed easily in their treat- ment. This opens a new avenue for the application of fuzzy model- ling rather than probabilistic, statistical or stochastic techniques, because regression method requires numerical data only. There- fore, fuzzy approach is suggested, developed and applied to drink- ing water consumption prediction in this paper. 0957-4174/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2009.04.028 * Corresponding author. Tel.: +90 212 285 6846; fax: +90 212 328 0400. E-mail address: altunkay@itu.edu.tr (A. Altunkaynak). Expert Systems with Applications 36 (2009) 11745–11752 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa