Murat Alper Basaran

Forecasting in high order fuzzy times series by using neural networks to define fuzzy relations

A given observation in time series does not only depend on preceding one but also previous ones in general. Therefore, high order fuzzy time series approach might obtain better forecasts than does first order fuzzy time series approach. Defining fuzzy relation in high order fuzzy time series approach are more complicated than that in first order fuzzy time series approach. A new proposed approach, which uses feed forward neural networks to define fuzzy relation in high order fuzzy time series, is introduced in this paper. The new proposed approach is applied to well-known enrollment data for the University of Alabama and obtained results are compared with other methods proposed in the literature. It is found that the proposed method produces better forecasts than the other methods.

A new approach for determining the length of intervals for fuzzy time series

In the implementations of fuzzy time series forecasting, the identification of interval lengths has an important impact on the performance of the procedure. However, the interval length has been chosen arbitrarily in many papers. Huarng developed a new approach which is called ratio-based lengths of intervals in order to identify the length of intervals. In our paper, we propose a new approach which uses a single-variable constrained optimization to determine the ratio for the length of intervals. The proposed approach is applied to the two well-known time series, which are enrollment data at The University of Alabama and inventory demand data. The obtained results are compared to those of other methods. The proposed method produces more accurate predictions for the future values of used time series.

Finding an optimal interval length in high order fuzzy time series

Univariate fuzzy time series approaches which have been widely used in recent years can be divided into two classes, which are called first order and high order models. In the literature, it has been shown that high order fuzzy time series approaches improve the forecasting accuracy. One of the important parts of obtaining high accuracy forecasts in fuzzy time series is that the length of interval is very vital. As mentioned in the first-order models by Egrioglu, Aladag, Basaran, Uslu, and Yolcu (2009), the length of interval also plays very important role in high order models too. In this study, a new approach which uses an optimization technique with a single-variable constraint is proposed to determine an optimal interval length in high order fuzzy time series models. An optimization procedure is used in order to determine optimum length of interval for the best forecasting accuracy, we used optimization procedure. In the optimization process, we used a MATLAB function employing an algorithm based on golden section search and parabolic interpolation. The proposed method was employed to forecast the enrollments of the University of Alabama to show the considerable outperforming results.

A new hybrid approach based on SARIMA and partial high order bivariate fuzzy time series forecasting model

In the literature, there have been many studies using fuzzy time series for the purpose of forecasting. The most studied model is the first order fuzzy time series model. In this model, an observation of fuzzy time series is obtained by using the previous observation. In other words, only the first lagged variable is used when constructing the first order fuzzy time series model. Therefore, this model can not be sufficient for some time series such as seasonal time series which is an important class in time series models. Besides, the time series encountered in real life have not only autoregressive (AR) structure but also moving average (MA) structure. The fuzzy time series models available in the literature are AR structured and are not appropriate for MA structured time series. In this paper, a hybrid approach is proposed in order to analyze seasonal fuzzy time series. The proposed hybrid approach is based on partial high order bivariate fuzzy time series forecasting model which is first introduced in this paper. The order of this model is determined by utilizing Box-Jenkins method. In order to show the efficiency of the proposed hybrid method, real time series are analyzed with this method. The results obtained from the proposed method are compared with the other methods. As a result, it is observed that more accurate results are obtained from the proposed hybrid method.

A new approach based on artificial neural networks for high order multivariate fuzzy time series

Fuzzy time series methods have been recently becoming very popular in forecasting. These methods can be categorized into two subclasses that are univariate and multivariate approaches. It is a known fact that real time series data can actually be affected by many factors. In this case, the using multivariate fuzzy time series forecasting model can be more reasonable in order to get more accurate forecasts. To obtain fuzzy forecasts when multivariate fuzzy time series approach is adopted, the most applied method is using tables of fuzzy relations. However, employing this method is a computationally though task. In this study, we introduce a new method that does not require using fuzzy logic relation tables in order to determine fuzzy relationships. Instead, a feed forward artificial neural network is employed to determine fuzzy relationships. The proposed method is applied to the time series data of the total number of annual car road accidents casualties in Belgium from 1974 to 2004 and a comparison is made between our proposed method and the methods proposed by Jilani and Burney [Jilani, T. A., & Burney, S. M. A. (2008). Multivariate stochastic fuzzy forecasting models. Expert Systems with Applications, 35, 691-700] and Lee et al. [Lee, L.-W., Wang, L.-H., Chen, S.-M., & Leu, Y.-H. (2006). Handling forecasting problems based on two factors high order fuzzy time series. IEEE Transactions on Fuzzy Systems, 14, 468-477].

A new approach based on the optimization of the length of intervals in fuzzy time series

In fuzzy time series analysis, the determination of the interval length is an important issue. In many researches recently done, the length of intervals has been intuitively determined. In order to efficiently determine the length of intervals, two approaches which are based on the average and the distribution have been proposed by Huarng [4]. In this paper, we propose a new method based on the use of a single variable constrained optimization to determine the length of interval. In order to determine optimum length of interval for the best forecasting accuracy, we used a MATLAB function which is employing an algorithm based on golden section search and parabolic interpolation. Mean square error is used as a measure of forecasting accuracy so the objective function value is mean square error value for forecasted observations. The proposed method was employed to forecast the enrollments of the University of Alabama to show the considerable outperforming results.

The effect of neighborhood structures on tabu search algorithm in solving course timetabling problem

The course timetabling problem must be solved by the departments of Universities at the beginning of every semester. It is a though problem which requires department to use humans and computers in order to find a proper course timetable. One of the most mentioned difficult nature of the problem is context dependent which changes even from departments to departments. Different heuristic approaches have been proposed in order to solve this kind of problem in the literature. One of the efficient solution methods for this problem is tabu search. Different neighborhood structures based on different types of move have been defined in studies using tabu search. In this paper, the effects of moves called simple and swap on the operation of tabu search are examined based on defined neighborhood structures. Also, two new neighborhood structures are proposed by using the moves called simple and swap. The fall semester of course timetabling problem of the Department of Statistics at Hacettepe University is solved utilizing four neighborhood structures and the comparison of the results obtained from these structures is given.

Improving weighted information criterion by using optimization

Although artificial neural networks (ANN) have been widely used in forecasting time series, the determination of the best model is still a problem that has been studied a lot. Various approaches available in the literature have been proposed in order to select the best model for forecasting in ANN in recent years. One of these approaches is to use a model selection strategy based on the weighted information criterion (WIC). WIC is calculated by summing weighted different selection criteria which measure the forecasting accuracy of an ANN model in different ways. In the calculation of WIC, the weights of different selection criteria are determined heuristically. In this study, these weights are calculated by using optimization in order to obtain a more consistent criterion. Four real time series are analyzed in order to show the efficiency of the improved WIC. When the weights are determined based on the optimization, it is obviously seen that the improved WIC produces better results.

A novel hybrid method for better evaluation: Evaluating university instructors teaching performance by combining conventional content analysis with fuzzy rule based systems

Even though engineering and applied sciences deal with numerical data, they have successfully implemented fuzzy logic by using fuzzy rule based (FRB) systems by verbalizing data. On the other hand, social sciences such as sociology, education and physiology transform verbal type data into numerical values by using Likert type scale. Despite the fact that fuzzy set theory deals with verbal data very powerfully, social science fields in general have avoided to implement it to their verbal data up until now. One of the most active research areas in education field which generates verbal data is student evaluation of teaching (SET) questionnaires which are related to Total Quality Management applications in most of the competitive universities in the world. In this paper, we propose a novel hybrid method, which combines conventional content analysis (CCA) method and FRB systems and this new hybrid method is more suitable for the verbal data obtained from SET questionnaires. This novel CCA-FRB (conventional content analysis based fuzzy rule based systems) method uses a sample of 138 junior students from Gazi University in Turkey to implement the proposed method.

Investigation of Structure-Activity Relationship Between Chemical Structure and CCR5 Anti HIV-1 Activity in a Class of 1-[N-(Methyl)-N- (Phenylsulfonyl)Amino]-2-(Phenyl)-4-[4-(Substituted)Piperidin-1-yl]Butane Derivatives: The Electronic-Topological Approach

The relationship between chemical structure and CCR5 anti HIV-1 activity was investigated in the series of 1-[N-(Methyl)-N-(phenylsulfonyl)amino]-2-(phenyl)-4-[4-(substituted) piperidin-1-yl]butanes derivatives including 114 molecules by using the Electron-Topological Method (ETM). In the frameworks of this approach, its input data were taken as the results of conformational and quantum-mechanical calculations. Conformational analysis and quantum-chemical calculations were carried out for each molecule. Then molecular fragments being specific for active molecules and non-active molecules were revealed by using ETM. The result of testing showed the high ability of ETM in predicting the activity and inactivity investigated series. In order to classify and to develop a model for those molecules, cluster and discriminant analyses are conducted. First, cluster analysis is implemented in order to classify similar molecules into the groups. Then, discriminant analysis is used to construct models including descriptors. By doing so, two obtained discriminant functions segregate those molecules into three different groups by using the descriptors called EHOMO, Dipole Moment and SEZPE.