; Ferdinando Di Martino. Time Series Seasonal Analysis Based on Fuzzy Transforms

A Summary of F-Transform Techniques in Data Analysis

Fuzzy transform is a technique applied to approximate a function of one or more variables applied by researchers in various image and data analysis. In this work we present a summary of a fuzzy transform method proposed in recent years in different data mining disciplines, such as the detection of relationships between features and the extraction of association rules, time series analysis, data classification. After having given the definition of the concept of Fuzzy Transform in one or more dimensions in which the constraint of sufficient data density with respect to fuzzy partitions is also explored, the data analysis approaches recently proposed in the literature based on the use of the Fuzzy Transform are analyzed. In particular, the strategies adopted in these approaches for managing the constraint of sufficient data density and the performance results obtained, compared with those measured by adopting other methods in the literature, are explored. The last section is dedicated to final considerations and future scenarios for using the Fuzzy Transform for the analysis of massive and high-dimensional data.

Seasonal Time Series Forecasting by F1-Fuzzy Transform

We present a new seasonal forecasting method based on F¹-transform (fuzzy transform of order 1) applied on weather datasets. The objective of this research is to improve the performances of the fuzzy transform-based prediction method applied to seasonal time series. The time series’ trend is obtained via polynomial fitting: then, the dataset is partitioned in S seasonal subsets and the direct F¹-transform components for each seasonal subset are calculated as well. The inverse F¹-transforms are used to predict the value of the weather parameter in the future. We test our method on heat index datasets obtained from daily weather data measured from weather stations of the Campania Region (Italy) during the months of July and August from 2003 to 2017. We compare the results obtained with the statistics Autoregressive Integrated Moving Average (ARIMA), Automatic Design of Artificial Neural Networks (ADANN), and the seasonal F-transform methods, showing that the best results are just given by our approach.