Fuzzy transforms method and attribute dependency in data analysis

Semiring-Valued Fuzzy Sets and F-Transform

The notion of a semiring-valued fuzzy set is introduced for special commutative partially pre-ordered semirings, including basic operations with these fuzzy structures. It is showed that many standard MV-algebra-valued fuzzy type structures with standard operations, such as hesitant, intuitionistic, neutrosophic or fuzzy soft sets are, for appropriate semirings, isomorphic to semiring-valued fuzzy sets with operations defined. F-transform and inverse F-transform are introduced for semiring-valued fuzzy sets and properties of these transformations are investigated. Using the transformation of MV-algebra-valued fuzzy type structures to semiring-valued fuzzy sets, the F-transforms for these fuzzy type structures is introduced. The advantage of this procedure is, among other things, that the properties of this F-transform are analogous to the properties of the classical F-transform and because these properties are proven for any semiring-valued fuzzy sets, it is not necessary to prove them for individual fuzzy type structures.

Fuzzy Transforms for Hesitant, Soft or Intuitionistic Fuzzy Sets

Classical F-transform for lattice-valued fuzzy sets can be defined using monadic relation in Zadeh’s monad or, equivalently, as a special semimodule homomorphism. In this paper, we use an analogical approach and by choosing suitable monads and semimodule homomorphisms, we define F-transform for hesitant, intuitionistic or fuzzy soft sets. We prove that these F-transforms naturally extend classical lattice-valued F-transform for lattice-valued fuzzy sets.

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.

Attribute dependency data analysis for massive datasets by fuzzy transforms

We present a numerical attribute dependency method for massive datasets based on the concepts of direct and inverse fuzzy transform. In a previous work, we used these concepts for numerical attribute dependency in data analysis: Therein, the multi-dimensional inverse fuzzy transform was useful for approximating a regression function. Here we give an extension of this method in massive datasets because the previous method could not be applied due to the high memory size. Our method is proved on a large dataset formed from 402,678 census sections of the Italian regions provided by the Italian National Statistical Institute (ISTAT) in 2011. The results of comparative tests with the well-known methods of regression, called support vector regression and multilayer perceptron, show that the proposed algorithm has comparable performance with those obtained using these two methods. Moreover, the number of parameters requested in our method is minor with respect to those of the cited in the above two algorithms.

Time Series Seasonal Analysis Based on Fuzzy Transforms

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 an assigned output. In the first example, we use the daily weather dataset of the municipality of Naples (Italy) starting from data collected from 2003 to 2015 making predictions on mean temperature, max temperature and min temperature, all considered daily. In the 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, Auto Regressive Integrated Moving Average (ARIMA) and the usual fuzzy transforms concluding that the best results are obtained under our approach in both examples. In addition, the comparison results show that, for seasonal time series that have no consistent irregular variations, the performance obtained with our method is comparable with the ones obtained using Support Vector Machine- and Artificial Neural Networks-based models.