# DEVELOPMENT OF A FUZZY TIME SERIES MODEL

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## DEVELOPMENT OF A FUZZY TIME SERIES MODEL

Chapter One:

Introduction

1.1 Background

Fuzzy time series (FTS) approaches are used in research, engineering, and general applications to create prediction models for weather, predictive control, signal processing, population forecasting, enrollment, and finance, among other things (Panagiotakis et al., 2016).

Forecasting can be described as predicting what will happen in the future. Researchers believe that no matter what technique is utilised, a flawless forecast will never be possible. Meanwhile, the goal of forecasting is to create a prediction model that will produce a more accurate forecasting result or a less error-prone result than those found in the literature.

There are three types of forecasting methods: qualitative, quantitative, and causal (Singh, 2016). When historical data on a forecasting variable is unavailable or inapplicable, the required method is known as qualitative forecasting (Singh 2016).

To generate a forecast, this method involves the judgement of an expert in that field or sector. On the other hand, if previous knowledge about the variable being anticipated is accessible and quantifiable, the required method is known as quantitative forecasting (Singh 2016).

In the latter scenario, forecasts are created using the time series method. A time series forecasting method is one in which historical data is limited to past values of the variable to be forecasted (Yusuf et al. 2015).

Causal forecasting approaches are prediction methods that assume a cause-and-effect relationship between the output variable (forecast) and one or more variables (Anderson et al., 2015).

2. Forecasting Eğrioglu et al. (2016) categorise techniques as probability theory-based (traditional), computational, fuzzy time series, and hybrid forecasting.

Traditional methods for solving time series forecasting problems include linear moving average (MA) models, auto-regressive (AR) models, and linear auto-regressive integrated moving average (ARIMA) models (Smith & Wunsch, 2015).

Such forecasting systems necessitate more observations and are unable to handle prediction issues in which historical data must be represented by linguistic values (Huang et al., 2011; Shah, 2012; Song & Chissom, 1993a).

Furthermore, such algorithms are limited to linearity assumptions alone (Shah, 2012), resulting in substantial inaccuracies in anticipated values.

FTS forecasting techniques have received a great deal of attention in recent years. However, prior techniques (Singh, 2016) had difficulties, including inaccurate interval length determination.

ii. Ignorance of recurring fuzzy logic linkages.

iii. The incorrect assigning of equal importance to fuzzy logic relationships.

iv. Use of first-order fuzzy logic linkages.

v. Calculating the defuzzified forecast output.

As a result, there is a need for a reliable prediction technique that can extract relevant information from limited historical data.
Soft Computing (SC) strategies have been used to address various issues presented by FTS modelling techniques (Singh, 2016).

The primary SC techniques for this purpose are Artificial Neural Network (ANN), Rough Set (RS), and Evolutionary Computing (EC). According to Singh (2016), all three offer effective solutions for tackling domain-specific issues.

The combination of various strategies results in the development of a hybrid technique, which is more advantageous than traditional procedures since it gives a sturdy, cost-effective, and approximate answer. However, this combination should be computationally efficient and easy to implement (Singh, 2016).

Clustering techniques such as K-means and fuzzy C-means have been used to overcome various subjective decisions made during the fuzzification of FTS, such as interval length, discourse universe, and membership value selection, to name a few.

These enhance FTS predicting accuracy. Cat Swarm Optimisation (CSO) was created to address the issue of premature convergence found in the aforementioned clustering techniques (Chu & Tsai, 2007).

In this study, CSO-C will be used in the fuzzification step to objectively identify the interval length, provide objective judgement in selecting the number of partitions, and demonstrate a good membership function between the items in a fuzzy set. PSO will be used during the defuzzification stage to assign optimal weights to elements of fuzzy forecasting rules.

1.2 Statement of Problem

Arbitrary decisions such as static interval lengths, parametric partitioning of the discourse universe at the fuzzification level, and giving weights to recurrent fuzzy rules all have an impact on the accuracy of FTS forecasting results.

It has become important to develop a FTS forecasting technique that optimises the partitioning of the universe of discourse into uneven interval lengths, handles recurrent fuzzy rules, and gives optimal weights to forecasting rule elements.

Using CSO-C algorithm for fuzzification, FSGs to build logical linkages, and PSO algorithm for defuzzification can increase fuzzy time series forecasting accuracy.

1.3 Aims and Objectives

The goal of this study is to create a fuzzy time series forecasting model that improves forecasting accuracy by combining Cat Swarm Optimisation Clustering (CSO-C) and Particle Swarm Optimisation. The research aims are as follows:
i. To create a FTS forecasting technique using CSO-C and PSO.

ii. Use the created FTS forecasting technique to forecast enrolment at the University of Alabama, Belgium road accident, and Taiwan Future Exchange datasets.

iii. Compare the results achieved using the created hybrid forecasting technique to those obtained using the FCM-based fuzzy time series technique, and validate using enrolment data from the University of Maiduguri and monthly temperature data from Jigawa state.

1.4 Scope of Research
This paper describes the construction of a hybrid FTS forecasting model that is empirically capable of forecasting univariate data and produces increased accuracy of findings when RMSE and MAPE are used as performance metrics.

To compare the performance of existing forecasting models with the created model, three standard data sets were used: Belgium vehicle road accident data, University of Alabama student enrolment data, and Taiwan future exchange (TAIFEX) data from the literature.

As a result, the model performance was evaluated using two data sets: UNIMAID student enrollment data and Jigawa state monthly temperature data.
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