Application of Fuzzy Sets and Shadowed Sets in Predicting Time Series Data

Application of Fuzzy Sets and Shadowed Sets in Predicting Time Series Data

Mahua Bose (University of Kalyani, India) and Kalyani Mali (University of Kalyani, India)
DOI: 10.4018/978-1-5225-5396-0.ch014
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In recent years, several methods for forecasting fuzzy time series have been presented in different areas, such as stock price, student enrollments, climatology, production sector, etc. Choice of data partitioning technique is a central factor and it highly influences the forecast accuracy. In all existing works on fuzzy time series model, cluster with highest membership is used to form fuzzy logical relationships. But the position of the element within the cluster is not considered. The present study incorporates the idea of fuzzy discretization and shadowed set theory in defining intervals and uses the positional information of elements within a cluster in selection of rules for decision making. The objective of this work is to show the effect of the elements, lying outside the core area on forecast. Performance of the presented model is evaluated on standard datasets.
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2. Literature Survey

In Fuzzy time series models, partitioning of universe of discourse is a crucial issue. There are two types of interval generation techniques: (1) equal-sized intervals and (2) unequal-sized intervals. In the studies made by earlier researchers, universe of discourse is directly partitioned into equal-sized intervals. Gradually, researchers shift their focus towards variable length intervals. These techniques can be classified into different categories depending upon the methodology adopted for the creation of intervals/clusters. Clusters can be created by applying (1) clustering algorithm directly (2) generating mathematical models (3) Using Evolutionary techniques namely genetic algorithms, particle swarm optimization. It is observed from literature review that unequal-sized partitioning techniques produce better forecasting accuracy than equal-sized partitioning techniques.

Studies that attempt variable sized data partitioning techniques include Distribution-and average-based partitioning (Huarng, 2001), recursive partition level by level (Li & Chen, 2004), two-phase partitioning (Chen & Hsu, 2004) “ratio-based” partitioning (Huarng & Yu, 2006), automatic clustering algorithm (Chen & Tanuwijaya, 2011), “minimize entropy principle approach” and “Trapezoid fuzzification approach” (Cheng et al., 2006), “Mean-Based Discretization” (Singh & Borah, 2013a), and “Re-Partitioning Discretization’’ approach (Singh & Borah,2013b), “Dynamic time warping distance (Wang et al., 2015) have been proposed. Recently, many forecasting models using the concept of information granule have been presented by Wang et al. (2013, 2014), Wang et al. (2015), Lu et al. (2014, 2015) and Chen and Chen (2015). Entropy discretization techniques (Chen and Chen, 2014) have also been presented.

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