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DEVELOPMENT OF A FUZZIFIED-TREND MAPPING AND IDENTIFICATION

DEVELOPMENT OF A FUZZIFIED-TREND MAPPING AND IDENTIFICATION

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DEVELOPMENT OF A FUZZIFIED-TREND MAPPING AND IDENTIFICATION

Chapter one

INTRODUCTION: 1.1 Preamble
A time series is merely a collection of quantitative data measured at regular periods of time. Time series, whether discrete or continuous, are inherently nonlinear and nonstationary since they are sample functions derived from stochastic processes (Subanar and Abadi, 2011).

Time series analysis and forecasting are critical in planning, equipment maintenance and optimisation, efficient quality of service (OoS), and even anomaly detection in a variety of fields, including engineering, medicine, the stock market, and information and communication technology (ICT) (Sah and Konstantin, 2005; Klevecka, 2011; Zhani et al., 2011; Cortez et al., 2012).

Time series forecasting has been extensively examined and investigated during the last three decades (Box and Jenkins, 1976; Song and Chissom, 1993a; Huarng and Yu, 2003; Wang et al., 2008; Singh and Borah, 2013).

In layman’s words, time series forecasting is the process of analysing historical time series data and predicting future variables based on that data (Box and Jenkins, 1976; Hassan et al., 2012). Traditionally, time series forecasting problems have been tackled with a class of statistical linear autoregressive (AR), moving average (MA), and hybrid (ARMA) models.

These models, as well as its following extensions, such as auto-regressive integrated moving average (ARIMA) and other linear models, are based on the assumption that time series are linear and stationary.

Soft computing techniques are a promising alternative to traditional linear techniques since they can approximate any genuine continuous function without making assumptions about the data’s structure (Subanar and Abadi, 2011).

Fuzzy logic has gained popularity because to its advantages over other techniques like neural networks and evolutionary algorithms (Song and Chissom, 1993a; Chabaa and Zeroual, 2009; Shah, 2012).

Among several essential challenges in fuzzy time series (FTS) models, trend mapping and identification have not been completely exploited by the academic community. This study focuses on the creation of a robust FTS forecasting model using a trend mapping and identification approach.

1.2 Motivation.
Time series analysis and forecasting are two ways humans attempt to exert some control over the future in order to avoid disasters, increase capacity, and efficiently manage and maximise precious resources.

Although time series analysis and forecasting have garnered the most attention in engineering, they apply to practically every aspect of human endeavour (Sah and Konstantin, 2005). The challenges of analysing and training vast amounts of historical time series data are a major concern in time series forecasting (Hassan et al., 2012).

Another key obstacle in solving time series forecasting difficulties is the nonlinear character of time series, as well as the highly unpredictable causative elements.

As a result, linear techniques and models frequently fail to meet the fundamental requirements for effective time series analysis and forecasting, such as prediction accuracy. Furthermore, because linear models require that the underlying generation process of time series is time invariant, they cannot be applied to every time series (Subanar and Abadi, 2011).

One important strategy to circumvent these drawbacks in linear techniques is to employ nonlinear techniques that do not require a big amount of training data and can analyse time series events in ways that humans think, namely in language terms.

Fuzzy logic, more than any other nonlinear technique, has demonstrated robustness and efficiency in dealing with time series forecasting problems (Shahida et al., 2003; Chabaa and Zeroual, 2009; Shah, 2012).

As a universal approximator, fuzzy systems have the benefit that the produced models are characterised by both numerical and

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