# An Empirical Study Of Fuzzy Approach With Artificial-Books Pdf

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INTERNATIONAL JOURNAL OF MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. fuzzy logical relationship is defined as In both models note that the establishment of fuzzy. relationships R t 1 t and defuzzification were the critical. Ai A j steps for forecasting 3 4 5 8 18 44, We used the following steps in problem solution. where Ai is named as left hand side of the fuzzy logical Step 1 Defining and partitioning the universe of discourse. Step 2 Fuzzification, relationship and A j the right hand side Note the repeated Step 3 Neural Network Training. fuzzy logical relationships are removed 3 43 Step 4 Neural Network Forecasting. Definition 4 Fuzzy logical relationships can be further Step 5 Defuzzification. grouped together into fuzzy logical relationship groups Step 6 Performance Evaluation. according to the same left hand sides of the fuzzy logical. relationships III ARTIFICIAL NEURAL NETWORKS, For example there are fuzzy logical relationships with the In forecasting artificial neural networks are mathematical. same left hand sides Ai models that imitate biological neural networks Artificial. neural networks consist of some elements Determining the. elements of the artificial neural networks issue that affect the. Ai Aj1 forecasting performance of artificial neural networks should be. Ai Aj 2 considered carefully 27 28 One of them is network. architecture However there are not general rules for. determining the best architecture So much architecture should. be tried for the correct results There are various types of. These fuzzy logical relationships can be grouped into a. artificial neural networks Let give an overview of the. fuzzy logical relationship group as follows, networks which is indicated in the best three networks for the. related data of the recent study 20 21, Ai Aj1 Aj 2.
Multi Layer Percepteron MLP MLP networks are, constructed of multiple layers of computational units Each. Definition 5 Suppose F t is caused by F t 1 only neuron in one layer is directly connected to the neurons of the. subsequent hidden layer In many applications the frequently. and F t F t 1 R t 1 t For any t if R t 1 t is used activation function is sigmoid function Multi layer. independent of t then F t is named a time invariant fuzzy networks use a variety of learning techniques the most popular. being back propagation, time series otherwise a time variant fuzzy time series. Artificial Neural Networks usually refer to Multilayer. Song and Chissom applied both time invariant and time. Perceptron Neural Networks and are a popular estimator to. variant models to forecast the enrollment at the University of. construct nonlinear models of data A MLP distinguishes itself. Alabama 3 4 The time invariant model includes the, by the presence of one or more hidden layers whose. following steps, computation nodes are correspondingly called hidden neurons. 1 define the universe of discourse and the intervals. of hidden units For example a three layer MLP is given in. 2 partition the intervals, Fig 1 The function of hidden neurons is to intervene.
3 define the fuzzy sets, between the external input and the network output in some. 4 fuzzify the data, useful manner 29, 5 establish the fuzzy relationships. MLP has been applied successfully to difficult problems by. 6 forecast, training in a supervised algorithm known as the error. 7 defuzzify the forecasting results, backpropagation algorithm This learning algorithm consists of. The time variant model includes the following steps. two directions through the different layers of the network. 1 Define the universe of discourse and the intervals the. forward and backward directions In the forward direction an. same as step 1 in the time invariant model, input data is applied to the input nodes of the network and its.
2 Partition the intervals the same as step 2 in the time. error propagates through the network layer by layer Finally a. invariant model, set of outputs is produced as an actual response of the network. 3 Define the fuzzy sets the same as step 3 in the time. During the forward direction the synaptic weights of the. invariant model, networks are not changed while during the backward. 4 Fuzzify the data the same as step 4 in the time, direction the synaptic weights are altered in accordance with. invariant model, an error correction rule The definite response of the output. 5 Establish the fuzzy relationships and forecast, layer is subtracted absolutely from an expected response to.
6 Defuzzify the forecasting results, produce an error signal This error signal is then propagated. backward through the network 21, Issue 1 Volume 6 2012 115. INTERNATIONAL JOURNAL OF MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. Training the MLP network with the backpropagation rule. guarantees that a local minimum of the error surface is found. though this is not necessarily the global one In order to speed. up the training process a momentum term is often introduced. into the update formula 42, wij t 1 a pi pj wij t 5. Radial Basis Function RBF That network type is, consisting of an input layer a hidden layer of radial units and. an output layer of linear units Typically the radial layer has. exponential activation functions and the output layer a linear. activation functions, Figure 1 Architecture of a three layer MLP RBF network is an alternative to the more widely used MLP.
network and is less computer time consuming for network. During the processing in a MLP network activations are training RBF network consists of three layers an input layer. propagated from input units through hidden units to output a hidden layer and an output layer The nodes within each. units At each unit j the weighted input activations ai wij are layer are fully connected to the previous layer The input. variables are each assigned to the nodes in the input layer and. summed and a bias parameter j is added they pass directly to the hidden layer without weights The. transfer functions of the hidden nodes are RBF 30, net j ai wij j. RBF networks are being used for function approximation. pattern recognition and time series prediction problems Such. networks have the universal approximation property 31 are. dealt well in the theory of interpolation 32 and arise naturally. The resulting network input net j is then passed through a as regularized solutions of ill posed problems 33 Their. sigmoid function the logistic function in order to restrict the simple structure enables learning in stages gives a reduction in. value range of the resulting activation a j to the interval 0 1 the training time and this has led to the application of such. networks to many practical problems 34, RBF networks have traditionally been associated with radial. 1 functions in a three layer network see Fig 2 consisting of an. 1 e j input layer a hidden layer of radial units and an output layer of. linear units 35 36, The network learns by adapting the weights of the. connections between units until the correct output is. produced MLP networks use a variety of learning techniques. the most popular being back propagation 21 It performs a. gradient descent search on the error surface The weight. update wij i e the difference between the old and the new. value of weight wij is here defined as, wij a pi pj 3. a pj 1 a pj t pj a pj if j is an output unit, a pj 1 a pj pk w jk if j is a hidden unit.
Figure 2 Architecture of a RBF Network, here t p is the target output vector which the network must. The radial basis function determines the output with input. Issue 1 Volume 6 2012 116, INTERNATIONAL JOURNAL OF MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. variable x and distance from center As the input variable. approaches the center the output becomes larger As the radial. basis function the Gaussian function is often used It may be. written as, where x input center width of receptive field. Output of RBF network is expressed by a linear combination. of the radial basis functions It may be written as. Figure 3 General structure of the GRNN, IV EMPIRICAL ANALYSIS. This study uses weekly closed prices of the exchange rate of. where w j connection weight j output of basis, TL to Euro between 2005 and 2009 as the forecasting target.
function 45 Empirical analysis shows preparing a neural network based. fuzzy time series model to improve forecasting performance. Generalized Regression Neural Networks GRNN That and show forecasting performance year by year according to. type of networks is a kind of Bayesian network GRNN has performance measure called mean square error MSE After. exactly four layers input a layer of radial centers a layer of obtaining all results we compared the results for all artificial. regression units and output This layer must be trained by a neural networks by using MSE from 2005 to 2009 and. clustering algorithm Think of it as a normalized RBF network calculated overall results. in which there is a hidden unit centered at every training case We can explain all steps for problem solution. A GRNN is based on nonlinear regression theory and often Step 1 Defining and partitioning the universe of. used as a popular statistical tool for function approximation discourse. GRNN is one variant of the RBF network unlike the standard The universe of discourse for observations. RBF the weights of these networks can be calculated U starting ending is defined After the length of intervals. analytically 37, GRNN was devised by Specht 38 casting a statistical l is determined the U can be partitioned into equal length. method of function approximation into a neural network form intervals u1 u2 ub b 1 and their corresponding. The GRNN like the MLP is able to approximate any midpoints m1 m2 mb respectively. functional relationship between inputs and outputs 39. Structurally the GRNN resembles the MLP However unlike. the MLP the GRNN does not require an estimate of the ub starting b 1 l starting b l. number of hidden units to be made before training can take starting b 1 l starting b l. place Furthermore the GRNN differs from the classical MLP mb. in that every weight is replaced by a distribution of weight. which minimizes the chance of ending up in local minima. We can show different length of intervals with starting and. Therefore no test and verification sets are required 40. ending points according to exchange rate of TL to Euro for all. GRNN has exactly four layers input a layer of radial. years in Table 1, centers a layer of regression units and output This layer must. be trained by a clustering algorithm Think of it as a. Table 1 Length of intervals for all years, normalized RBF network in which there is a hidden unit. Start End Interval Length, centered at every training case Figure 3 shows the general. 2005 1 58 1 86 0 28 0 02, structure of the GRNN 41.
2006 1 55 2 11 0 56 0 04, 2007 1 67 1 89 0 22 0 02. 2008 1 7 2 22 0 52 0 04, 2009 2 05 2 29 0 24 0 02, For example for the year 2005 we have U 1 58 1 86. Issue 1 Volume 6 2012 117, INTERNATIONAL JOURNAL OF MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. and the length of interval is set to 0 02 The relation of these has advantage to improve forecasting. Step 2 Fuzzification performance especially in handling nonlinear systems Hence. Each linguistic observation Ai can be fuzzified into a set in this study we aimed to handle a nonlinear problem to apply. neural network based fuzzy time series model Differing from. of degrees of membership, previous studies we used various degrees of membership in. establishing fuzzy relationships and we performed different. A1 11 u1 12 u2 1b ub neural network models to improve forecasting performance. To demonstrate comparison between these models we used a. Step 3 Neural Network Training data set of exchange rate of Turkish Liras TL to Euro for the. A large data set is necessary for training a neural network years 2005 2009 Empirical results show that the multilayer. and we used weekly closing prices of the exchange rate of TL perceptron is the best to forecast fuzzy time series in most. to Euro for the years from 2005 to 2009 Many studies have commonly used artificial neural network models. used a convenient ratio to separate in samples from out of Time series forecasting by using artificial neural networks is. samples ranging from 70 30 to 90 10 Hence we an important issue in many scientific researches in recent. chose the data from January to October for our training in years Artificial neural networks are sufficient due to their. sample and November and December for forecasting out abilities to solve nonlinear problems nowadays. sample So the ratio is about 83 17 F t 1 Ai is taken In this paper we made a forecasting study for weekly closed. prices of the exchange rate of TL to Euro between 2005 and. as input and F t Aj is taken as output since fuzzy logical. 2009 which has important effect in economical and industrial. relationship is defined as Ai A j areas We applied the best four networks which are called. Step 4 Neural Network Forecasting MLP RBF and GRNN to improve forecasting fuzzy time. By applying the process we use all training data for training series with different degrees of membership by using MSE. the neural network so we can forecast all the degrees of performance measure. membership for out of sample data First by using the exchange rate of TL to Euro for the years. Artificial neural networks are sufficient due to their abilities to solve nonlinear problems nowadays In this paper we made a forecasting study for weekly closed prices of the exchange rate of TL to Euro between 2005 and 2009 which has important effect in economical and industrial areas We applied the best four networks which are called MLP RBF and GRNN to improve forecasting fuzzy time

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