Comprison of Fuzzy Possibilistic Regression and Fuzzy Least Square Regression Models to Estimate Groundwater Level of Neyshabour Aquifer

Document Type : Research Paper


1 M.Sc. Student of Water Resource Management, University of Birjand.

2 Associate Professor, Water Engineering Department, College of Agriculture, University of Birjand, Birjand, Iran


Groundwater has always been considered as one of the main sources of drinking, agriculture, and industrial water, especially in arid and semi-arid regions. Investigating groundwater level changes in any region has an important role in planning sustainable water resources management. Continuous decline of groundwater level has been observed worldwide in the past half-century. Groundwater is the most important and the only source of freshwater in Neyshabour plain. Unallowable discharges of the groundwater resources and the reduction of recharge factors have caused about 200 million cubic meters deficit in Neyshabour aquifer. Therefore, estimating groundwater is vitally important for the management of water resources.
This study was conducted in Neyshabour aquifer in Khorasan Razavi province situated between 58o13' to 59o30' eastern longitude and 35o40' to 36o39' northern latitude. Neyshabour plain has an important role in agricultural productions of Khorasan Razavi. In this study, the fuzzy possibilistic regression and fuzzy least square regression approaches were evaluated in order to forecast the groundwater changes in Neyshabour aquifer. For this propose, the parameters affecting aquifer level, including monthly precipitation, discharge detected, and fuzzy regression approaches were employed to estimate groundwater level of aquifer, and then raster maps were determined by geostatistical methods. Data bank was determined by Arc GIS software from raster maps to train and test fuzzy regression models. 50 percent of data was selected as calibration data and 50 percent of data was selected as validation data in each model. In linear regression, for each series of input variables, only a specific output value is computed, while fuzzy regression models estimate the boundaries of possible values for the output variables. Therefore, unlike the classical regression, which was based on probability theory, the fuzzy regression is based on possibility and fuzzy sets theory. Fuzzy possibilistic regression, introduced by Tanaka et al. (1982), is an approach that provides the best regression equation by minimizing the amount of fuzzy. The general form of this fuzzy regression function is as follows:

Ỹ  =Ã01X12X2+ Ã3X3+…+ÃnXn                                                                                                                                     


where Ã0 and Ã1 are the fuzzy intercept and fuzzy slope coefficients, respectively, and X is the independent variable and the output Ỹ (or dependent variable) is a fuzzy number. 
Fuzzy least-squares regression (FLSR) method as proposed by Savic and Pedrycz (1991) was adopted for this analysis. For the purpose of current study, the efficiency of the fuzzy possibilistic and fuzzy least square regression models for groundwater prediction in Neyshabour aquifer were compared. Validation and Verification of models were determined based on mean error (ME), root mean square error (RMSE), and coefficient of determination (R2).


Main Subjects

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Volume 43, Issue 1
March 2020
Pages 131-143
  • Receive Date: 14 February 2018
  • Revise Date: 24 April 2018
  • Accept Date: 28 April 2018
  • Publish Date: 20 March 2020