Development of a Fuzzy Time Series Model Using Cat Swarm Optimization Clustering and Optimized Weights of Fuzzy Relations
Development of a Fuzzy Time Series Model Using Cat Swarm Optimization Clustering and Optimized Weights of Fuzzy Relations.
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 models.
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 the 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%.
TABLE OF CONTENTS
INTRODUCTION
- Background……………………………………………………………………… 1
- Statement of Problem……………………………………………………………………… 3
- Aim and Objectives……………………………………………………………………… 4
- Scope of the Research……………………………………………………………………… 4
CHAPTER TWO: LITERATURE REVIEW
- Introduction……………………………………………………………………… 5
- Review of Fundamental Concepts……………………………………………………………………… 5
- Time Series……………………………………………………………………… 5
- Fuzzy Set Theory……………………………………………………………………… 5
- Universe of Discourse……………………………………………………………………… 7
- Membership Function……………………………………………………………………… 7
- Fuzzy time series……………………………………………………………………… 7
- Fuzzy Set Groups (FSGs)……………………………………………………………………… 9
- Defuzzification Operator……………………………………………………………………… 9
- Basic steps of fuzzy time series forecasting……………………………………………………………………… 10
- Data Clustering……………………………………………………………………… 10
- Cat Swarm Optimization (CSO)……………………………………………………………………… 11
- Seeking Mode……………………………………………………………………… 13
- Tracing Mode (Movement)……………………………………………………………………… 14
- Cat Swarm Optimization Clustering (CSO-C)……………………………………………………………………… 15
- Particle Swarm Optimization (PSO)……………………………………………………………………… 19
- Performance Indices……………………………………………………………………… 20
- Review of Similar Work……………………………………………………………………… 21
CHAPTER THREE: MATERIALS AND METHODS
- Introduction……………………………………………………………………… 25
- Materials……………………………………………………………………… 26
- Methods……………………………………………………………………… 26
- Development of an FTS forecasting technique based on CSO-C and PSO………………………………….. 27
- Application of the Developed FTS Technique to Forecast Data……………………………………. 33
- Forecasting Car Road Accident in Belgium…………………………………………………………. 34
- Forecasting Student Enrolment in the University of Alabama………………………………… 37
- Forecasting TAIFEX……………………………………………………………………… 39
- Forecasting Student Enrolment in UNIMAID………………………………………………… 41
- Forecasting Monthly Temperature in Jigawa State…………………………………………………. 44
- Comparison of Results Obtained with Existing Techniques……………………………………………… 46
CHAPTER FOUR: RESULTS AND DISCUSSION
- Introduction……………………………………………………………………… 47
- Forecasting Results for Car Road Accident……………………………………………………………………… 47
- Validation……………………………………………………………………… 54
- Significance of Forecasting Results……………………………………………………………………… 65
CHAPTER FIVE: SUMMARY, CONCLUSION, AND RECOMMENDATIONS
- Summary……………………………………………………………………… 66
- Significant Contributions……………………………………………………………………… 66
- Conclusion……………………………………………………………………… 67
- Recommendations for Further Works……………………………………………………………………… 68
REFERENCES……………………………………………………………………… 69
INTRODUCTION
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).
REFERENCES
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Bahrami, M., Bozorg-Haddad, O., & Chu, X. (2018). Cat Swarm Optimization (CSO) Algorithm. In O. Bozorg-Haddad (Ed.), Advanced Optimization by Nature-Inspired Algorithms (pp. 9-18). Fargo, North Dakota: Springer Nature Singapore Pte Ltd.
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CSN Team.
