ABSTRACT
This research developed a hybrid forecasting technique that integrates Cat Swarm Optimization Clustering (CSO-C) and Particle Swarm Optimization (PSO) algorithms with Fuzzy Time Series (FTS) forecasting model. Cat Swarm Optimization Clustering (CSO-C) which is an algorithm for data classification is adopted at the fuzzification stage to objectively partition the universe of discourse into unequal intervals. Then, disambiguated fuzzy relationships are obtained using Fuzzy Set Grouping (FSG). Finally, Particle Swarm Optimization (PSO) was adopted to optimize the defuzzification phase; by tuning weights assigned to fuzzy sets in a rule. This rule is a fuzzy logical relationship induced from a fuzzy set group (FSG). The clustering and optimization algorithms were implemented in MATLAB. Belgium road yearly accident data, Alabama University yearly student enrolment data, Taiwan future exchange data, University of Maiduguri (UNIMAID) yearly student enrolment data and Jigawa state yearly temperature data were collected and used to evaluate the developed hybrid model. To evaluate the forecasting efficiency of the developed hybrid model, its statistical performance metric of Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) were calculated and compared with previous techniques in the literature. Improvement was achieved in the developed forecasting technique, when compared with the benchmark Fuzzy Time Series (FTS) model of Qiang Song and Brad S. Chissom part I and II in forecasting student enrolment of University of Alabama. Results showed that an RMSE of 6.669 and MAPE result of 0.033%was obtained when compared with the benchmark work of Song and Chissom in student enrolment whose result was an RMSE of 650 and MAPE of 3.22%. There is also an improvement, in comparison to Fuzzy C-Means FTS based model of Yusuf et al (2015) whose result showed an RMSE of 7.02 and MAPE of 0.04%. The application of developed model on Belgium car road accident obtained an RMSE result of 5.931 and MAPE result of 0.346%which is an improvement over FCM based FTS model with RMSE of 19.2 and MAPE of 0.67%.Similarly, on application an RMSE of 2.571 and MAPE of 0.0375%were obtained in the forecast of University of Maiduguri student enrolment while in Jigawa monthly temperature forecast RMSE of 0.357 and MAPE of 0.1% were obtained. Relatively, the points on the plots followed a steady trend with the actual values for enrolment and temperature forecast respectively.
TABLE OF CONTENTS
DECLARATION
CERTIFICATION
DEDICATION
ACKNOWLEDGEMENTS
ABSTRACT
TABLE OF CONTENTS
LIST OF FIGURES
LIST OF TABLES
LIST OF APPENDICES
LIST OF ABBREVIATIONS
CHAPTER ONE: INTRODUCTION
1.1 Background 1
1.2 Statement of Problem 3
1.3 Aim and Objectives 4
1.4 Scope of the Research 4
CHAPTER TWO: LITERATURE REVIEW
2.1 Introduction 5
2.2 Review of Fundamental Concepts 5
2.2.1 Time Series 5
2.2.2 Fuzzy Set Theory 5
2.2.2.1 Universe of Discourse 7
2.2.2.2 Membership Function 7
2.2.3 Fuzzy time series 7
2.2.4 Fuzzy Set Groups (FSGs) 9
2.2.5 Defuzzification Operator 9
2.2.6 Basic steps of fuzzy time series forecasting 10
2.2.7 Data Clustering 10
2.2.8 Cat Swarm Optimization (CSO) 11
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2.2.8.1 Seeking Mode 13
2.2.8.2 Tracing Mode (Movement) 14
2.2.9 Cat Swarm Optimization Clustering (CSO-C) 15
2.2.10 Particle Swarm Optimization (PSO) 19
2.2.11 Performance Indices 20
2.3 Review of Similar Work 21
CHAPTER THREE: MATERIALS AND METHODS
3.1 Introduction 25
3.2 Materials 26
3.3 Methods 26
3.3.1 Development of an FTS forecasting technique based on CSO-C and PSO 27
3.3.2 Application of the Developed FTS Technique to Forecast Data 33
3.3.2.1 Forecasting Car Road Accident in Belgium 34
3.3.2.2 Forecasting Student Enrolment in University of Alabama 37
3.3.2.3 Forecasting TAIFEX 39
3.3.2.4 Forecasting Student Enrolment in UNIMAID 41
3.3.2.5 Forecasting Monthly Temperature in Jigawa State 44
3.3.3 Comparison of Results Obtained with Existing Techniques 46
CHAPTER FOUR: RESULTS AND DISCUSSION
4.1 Introduction 47
4.2 Forecasting Results for Car Road Accident 47
4.3 Validation 54
4.4 Significance of Forecasting Results 65
CHAPTER FIVE: SUMMARY, CONCLUSION AND RECOMMENDATIONS
5.1 Summary 66
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5.2 Significant Contributions 66
5.3 Conclusion 67
5.4 Recommendations for Further Works 68
REFERENCES 69
APPENDIX 71
CHAPTER ONE
ITRODUCTION
1.1 Background
Fuzzy time series (FTS) techniques are utilized in the fields of science, engineering and general applications to develop prediction models for weather forecasting, predictive control, signal processing, population forecasting, enrolment and finance among others (Panagiotakis et al., 2016).
Forecasting can be defined as the prediction of what is going to happen in the future. Researchers are of the opinion that regardless of the technique used, there can never be a perfect forecast. Meanwhile, the aim of forecasting is either to develop a prediction model that will lead to a more accurate forecasting result or an error reduced result compared to the ones in literature.
There are three classes of forecasting methods namely; qualitative, quantitative and causal (Singh, 2016). Whenever the historical data on a forecasting variable is not available or it is not applicable, the required method is referred to as qualitative forecast (Singh, 2016). This is a method that requires the judgement of an expert on that field or area to develop a forecast. On the other hand, if past information about the variable being forecasted is available and quantifiable, the required method is known as quantitative forecasting (Singh, 2016). In the latter case, forecasts are generated using time series method. The forecasting technique in which historical data is restricted to past values of the variable to be forecasted is called a time series forecasting method (Yusuf et al., 2015). Causal forecasting techniques are predictions methods that are based on the assumptions that the output variable (forecast) has a cause-effect relationship with one or more variables (Anderson et al., 2015).
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Forecasting Techniques can further be divided into; probability theory-based (conventional) methods, computational methods, fuzzy time series and hybrid forecasting methods (Eğrioglu et al., 2016).
Time series forecasting problems can be traditionally solved using linear moving average (MA) models, auto-regressive (AR) models and linear auto-regressive integrated moving average (ARIMA) models (Smith & Wunsch, 2015). Such forecasting techniques require larger observations and are unable to deal with prediction problems in which the historical data needs to be represented by linguistic values (Huang et al., 2011; Shah, 2012; Song & Chissom, 1993a). Also, such techniques are confined to linearity assumptions only (Shah, 2012), which introduces large errors in the predicted values.
FTS forecasting techniques have drawn a lot of attention in recent years. However, there are certain issues associated with the development of earlier techniques (Singh, 2016) such as;
i. Inaccurate determination of length of intervals.
ii. Ignorance of repeated fuzzy logic relationships.
iii. Inappropriate assignment of equal importance to fuzzy logic relationships.
iv. Utilization of first order fuzzy logic relationships.
v. Calculation of defuzzified forecast output.
Hence, there is the need for a robust prediction technique that can uncover useful information from little historical data.
Soft Computing (SC) techniques have been utilised to deal with different challenges imposed by FTS modelling techniques (Singh, 2016). The main SC techniques for this purpose include: Artificial Neural Network (ANN), Rough Set (RS) and Evolutionary Computing (EC). Each of
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them provides significant solution for addressing domain specific problems (Singh, 2016). The combination of these techniques leads to the development of a hybrid technique, which has more advantage, because it provides robust, cost effective and approximate solution, in comparison to traditional techniques. However, this combination should be computationally inexpensive and simple to implement (Singh, 2016).
Clustering techniques like K-means and fuzzy C-means have been utilized to overcome some subjective decisions made during fuzzification of FTS, such as; interval length, universe of discourse, choice of membership values, to mention but a few. These improve FTS forecasting accuracy. Cat Swarm Optimization (CSO) was developed to limit the shortcoming of premature convergence identified in the afore-mentioned clustering techniques (Chu & Tsai, 2007).
In this research CSO-C will be utilized in the fuzzification stage to objectively determine the interval length, provide objective judgement in choosing number of partitions and show good membership function between the elements in a fuzzy set. PSO will be utilized in the defuzzification stage to assign optimal weights to elements of fuzzy forecasting rules.
1.2 Statement of Problem
The accuracy of FTS forecasting result is affected by arbitrary decisions such as static interval lengths, parametric partitioning of universe of discourse at fuzzification level, and assigning weights to recurrent fuzzy rules. It has become necessary for an FTS forecasting technique that optimizes the partitions of universe of discourse into unequal interval length, deal with recurrent fuzzy rules and assigns optimal weights to elements of a forecasting rule. As a consequence, employing CSO-C algorithm in fuzzification, Fuzzy Set Groups (FSGs) to generate logical
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relationships and PSO algorithm in defuzzification will improve fuzzy time series forecasting accuracy.
1.3 Aim and Objectives
This research aims to develop a fuzzy time series forecasting model using Cat Swarm Optimization Clustering (CSO-C) and Particle Swarm Optimization (PSO) in order to improve forecasting accuracy. The objectives of the research are as follows:
i. To develop an FTS forecasting technique based on CSO-C and PSO.
ii. To apply the developed FTS forecasting technique to forecast enrolments at University of Alabama, Belgium road accident and Taiwan Future Exchange data sets.
iii. To compare the results obtained using the developed hybrid forecasting technique with results obtained using the FCM based fuzzy time series technique and to validate using university of Maiduguri enrolment data and monthly temperature data of Jigawa state.
1.4 Scope of the Research
This work covers the development of a hybrid FTS forecasting model which empirically has the capability of forecasting a univariate data that yields improved accuracy of results using RMSE and MAPE as performance metrics. In terms of comparison, the performance of previous forecasting models with the developed model considering three standard data sets namely; Belgium car road accident data, University of Alabama student enrolment data and Taiwan future exchange (TAIFEX) data in literature were considered. Consequently, the model performance was validated using two data sets namely; UNIMAID student enrolment data and Jigawa state monthly temperature data.
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