Comparison of the performance of Fuzzy-Inference System and integrated Fuzzy-Inference System- Monte Carlo models for predicting the distribution of drinking water sources in different districts of Kermanshah

Extended Abstract
 
Introduction
Shortage of high quality freshwater is one of the great challenges that human civilization is facing in the 21st century (Shiklomanov, 2000). This issue threatens the social welfare, public health and ecosystem health. On one hand, limited freshwater resources and increasing demand for this vital resource signifies water issue. On the other hand, non-uniformity of spatial and temporal distribution has complicated the management of these problems (Makhdoom, 1999). Climate change is also one of the main reason for worsening the quality and quantity of water while lowering groundwater level (Lambrakis, 2006). Therefore, good management of water resources to predict water demand for the future in different districts is needed. Accordingly, Multi Criteria Decision Making Method (MCDM) is used (Mousseau & Slowinski, 1998). The aim of this study is to compare the results of estimation of the Fuzzy Inference System and Fuzzy Inference System- Monte Carlo models for predicting drinking water demand in different districts of Kermanshah for the year 1400. Factors such as population growth, per capita water usage and urban development have been considered in order to the manage water resources and accurate planning of the Kermanshah city. This is the novelty of this research. In other words, at first the relation between distribution amount of water consumption and population distribution and after that, the relation between population distribution and the physical development of the city of Kermanshah are studied. That is according to physical development of the city, distribution amount of water consumption is determined.
Data and Methods
At first the parameters related to the research were determined by using expert opinions and previous research. The Electre method was used to reduce indicator numbers. After that Monte Carlo simulation was used for obtaining weighted indexes. Finally, for estimation of distribution of population and water demand, FIS method was employed. Ten indices affecting the population and amount of water were chosen according to previous researches. These identified parameters included slope, distance from the river, elevation, distance from pipelines water, distance from roads (roads- Avenue), a distance of the center of town, population density, land use, distance from the river. Due to existence of numerous gathered parameters, some of them were filtered as inputs for FIS model. For doing this, Electre model was considered to select more efficient indices based on the 40 experts’ opinions. Each index was weighed according to Likert scale. The most effective layer was labeled with "very importance" and the least effective layer with "little importance". For determining the index weight, Monte Carlo simulation method was used. FIS model was also employed to determine density population of districts of the city. FIS model was employed in two states: First, state as combination model in which the consequences of employed Monte Carlo method for weighting of different layers were assessed. In the second state, only FIS method was employed, because of equality in regarding index weights.
Conclusion and Discussion
Elimination of slope aspect, distance from the river and elevation comes from Electre method. It was mentioned that the Monte Carlo method is based on Saati Judgment, assigning to the accuracy of calculation (A=0/01). The value of T and N were calculated: T=%5 and N=10000. The result from FIS model and FIS-Monte Carlo model were considered to determine the amount of water that is needed for districts 1 to 3. Both models determined district 3 as the district that needs the maximum amount of water while district 1 with the minimum amount of water.
Conclusion
The evaluation of distribution of water demand for city is a very complicated issue that is influenced by a variety of parameters. These include the effect of population distribution such as natural factors, human infrastructure, policies in urban planning and urban development etc. Multi Criteria Decision Making (MCDM) method is commonly used to solve this problem. Because of high flexibility and power of their theory, fusion model are more efficient in counting complexity of problem (Shu, and Ouarda, 2008; Shahraki and Abbasian, 2014; Leyva and Fernandez, 2003; Asgharpour, 2012; Ghazanfari Rad, 2011; Rahmati et al., 2014; Sultan Panah and Farooq, 2000). So, these models are more efficient with respect to non-inclusive models. In this research two FIS and FIS-Monte Carlo methods were employed to estimate of population distribution and the amount of water demand with different results. According to the above explanation, the result of fusion model FIS-Monte Carlo is more reasonable. This reasonable result can be reported to the organizations that depend on water resources for future scheduling, management of water resources crisis.