Fuzzy regression analysis with non-symmetric fuzzy number coefficients and its neural network implementation

Author(s):  
H. Ishibuchi ◽  
M. Nii
Author(s):  
EBRAHIM NASRABADI ◽  
S. MEHDI HASHEMI

Some neural network related methods have been applied to nonlinear fuzzy regression analysis by several investigators. The performance of these methods will significantly worsen when the outliers exist in the training data set. In this paper, we propose a training algorithm for fuzzy neural networks with general fuzzy number weights, biases, inputs and outputs for computation of nonlinear fuzzy regression models. First, we define a cost function that is based on the concept of possibility of fuzzy equality between the fuzzy output of fuzzy neural network and the corresponding fuzzy target. Next, a training algorithm is derived from the cost function in a similar manner as the back-propagation algorithm. Last, we examine the ability of our approach by computer simulations on numerical examples. Simulation results show that the proposed algorithm is able to reduce the outlier effects.


2016 ◽  
Vol 74 (6) ◽  
pp. 1296-1311 ◽  
Author(s):  
Hossein Zangooei ◽  
Mohammad Delnavaz ◽  
Gholamreza Asadollahfardi

Coagulation and flocculation are two main processes used to integrate colloidal particles into larger particles and are two main stages of primary water treatment. Coagulation and flocculation processes are only needed when colloidal particles are a significant part of the total suspended solid fraction. Our objective was to predict turbidity of water after the coagulation and flocculation process while other parameters such as types and concentrations of coagulants, pH, and influent turbidity of raw water were known. We used a multilayer perceptron (MLP), a radial basis function (RBF) of artificial neural networks (ANNs) and various kinds of fuzzy regression analysis to predict turbidity after the coagulation and flocculation processes. The coagulant used in the pilot plant, which was located in water treatment plant, was poly aluminum chloride. We used existing data, including the type and concentrations of coagulant, pH and influent turbidity, of the raw water because these types of data were available from the pilot plant for simulation and data was collected by the Tehran water authority. The results indicated that ANNs had more ability in simulating the coagulation and flocculation process and predicting turbidity removal with different experimental data than did the fuzzy regression analysis, and may have the ability to reduce the number of jar tests, which are time-consuming and expensive. The MLP neural network proved to be the best network compared to the RBF neural network and fuzzy regression analysis in this study. The MLP neural network can predict the effluent turbidity of the coagulation and the flocculation process with a coefficient of determination (R2) of 0.96 and root mean square error of 0.0106.


2011 ◽  
Vol 181 (19) ◽  
pp. 4154-4174 ◽  
Author(s):  
Pierpaolo D’Urso ◽  
Riccardo Massari ◽  
Adriana Santoro

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