scholarly journals Multi-dimensional fuzzy transform and projection

2017 ◽  
Vol 307 ◽  
pp. 83-98 ◽  
Author(s):  
Jean-François Crouzet
Keyword(s):  
Fuzzy Transform

scholarly journals A Summary of F-Transform Techniques in Data Analysis

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1771
Author(s):  
Ferdinando Di Martino ◽  
Irina Perfilieva ◽  
Salvatore Sessa
Keyword(s):  
Data Analysis ◽  
Analysis Data ◽  
High Dimensional ◽  
Sufficient Data ◽  
Fuzzy Transform ◽  
Transform Method ◽  
Data Density ◽  
Fuzzy Partitions ◽  
Definition Of ◽  
Performance Results

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.

scholarly journals New Approximation Methods Based on Fuzzy Transform for Solving SODEs: II

2018 ◽  
Vol 1 (3) ◽  
pp. 30 ◽  
Author(s):  
Hussein ALKasasbeh ◽  
Irina Perfilieva ◽  
Muhammad Ahmad ◽  
Zainor Yahya
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Trapezoidal Rule ◽  
Approximation Methods ◽  
System Of Differential Equations ◽  
Fuzzy Transform ◽  
Fuzzy Partition ◽  
Fuzzy Approximation ◽  
One Step ◽  
Basic Functions

In this research, three approximation methods are used in the new generalized uniform fuzzy partition to solve the system of differential equations (SODEs) based on fuzzy transform (FzT). New representations of basic functions are proposed based on the new types of a uniform fuzzy partition and a subnormal generating function. The main properties of a new uniform fuzzy partition are examined. Further, the simpler form of the fuzzy transform is given alongside some of its fundamental results. New theorems and lemmas are proved. In accordance with the three conventional numerical methods: Trapezoidal rule (one step) and Adams Moulton method (two and three step modifications), new iterative methods (NIM) based on the fuzzy transform are proposed. These new fuzzy approximation methods yield more accurate results in comparison with the above-mentioned conventional methods.

scholarly journals Time Series Seasonal Analysis Based on Fuzzy Transforms

2017 ◽  
Author(s):  
Ferdinando Di Martino ◽  
Salvatore Sessa
Keyword(s):  
Time Series ◽  
Seasonal Forecasting ◽  
Weather Station ◽  
Fuzzy Transform ◽  
Italian Region ◽  
Mean Temperature ◽  
Forecasting Method ◽  
Seasonal Analysis ◽  
The Universe ◽  
Universe Of Discourse

We define a new seasonal forecasting method based on fuzzy transforms. We use the best interpolating polynomial for extracting the trend of the time series and generate the inverse fuzzy transform on each seasonal subset of the universe of discourse for predicting the value of a an assigned output. Like first example, we use the daily weather dataset of the municipality of Naples (Italy) starting from data collected from 2003 till to 2015 making predictions on the following outputs: mean temperature, max temperature and min temperature, all considered daily. Like second example, we use the daily mean temperature measured at the weather station “Chiavari Caperana” in the Liguria Italian Region. We compare the results with our method, the average seasonal variation, ARIMA and the usual fuzzy transforms concluding that the best results are obtained under our approach in both examples.

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