Fuzzy transform in the analysis of data

Perfilieva, Irina; Novák, Vilém; Dvořák, Antonı́n

doi:10.1016/j.ijar.2007.06.003

Cited by 116 publications

(85 citation statements)

References 6 publications

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“…The theory of F -transform was further elaborated and extended from real valued to lattice-valued functions (cf., [10,12]) and from fuzzy sets to parametrized fuzzy sets (cf., [17]). The theory of F -transform is successfully used in signal and image processing [7], compression [11], denoising [9], numerical solutions of partial differential equations [18], data analysis [13], and neural network approaches [19].…”

Section: Introductionmentioning

confidence: 99%

On the relationship among F-transform, fuzzy rough set and fuzzy topology

Perfilieva¹,

Singh²,

Tiwari³

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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The objective of this work is to associate the concepts of fuzzy rough sets and fuzzy topologies with fuzzy transform. It is shown here that the fuzzy transform can be viewed as fuzzy approximation operators studied in the operator-oriented view of fuzzy rough set theory and the use of fuzzy rough set results reduces efforts in proving fuzzy transform theoretic results. We present a glimpse that fuzzy topological results can also be used in similar fashion for fuzzy transform theoretical results.

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Section: Introductionmentioning

confidence: 99%

On the relationship among F-transform, fuzzy rough set and fuzzy topology

Perfilieva¹,

Singh²,

Tiwari³

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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“…The fuzzy transform (F-transform) has recently been introduced by I. Per…lieva in [3] (see also [4], [5], [6]) and its properties as a general smoothing tool have been illustrated in [8], [10], [1].…”

Section: F-transform and Its Propertiesmentioning

confidence: 99%

Expectile Smoothing using F.transform

Guerra

Stefanini

2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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In this paper, we will illustrate the F-transform based on generalized fuzzy partitions as a tool for expectile smoothing. This allows to represent a time series in terms of a fuzzy-valued function whose level-cuts are modeled by F-transform and estimated by expectile regression. The proposed methodology is illustrated on real economic and …-nancial time series.Keywords: Fuzzy Transform, Expectile Smoothing, Fuzzy Time Series F-transform and its propertiesThe fuzzy transform (F-transform) We brie ‡y recall the basic de…nitions and properties of the F-transform (see [3], [10]).Given a continuous function f : [a; b] ! R and given a …nite family of fuzzy sets (in particular fuzzy numbers) A = fA 1 ; A 2 ; :::; A n g forming a fuzzy partition of [a; b], the F-transform produces a vector of real numbers F = (F 1 ; F 2 ; :::; F n ) (called the direct F-transform). Each F k is the minimizer of a weighted squared error between the values f (x) and F k on the k th subinterval of [a; b]. The direct F-transform F is then used to de…ne the inverse Ftransform function b f : [a; b] ! R and the main result is that b f is an approximating function of f on [a; b].In the basic setting, each basic function A k of the fuzzy partition (P; A) has been considered to be zero outside the union of the two adjacent subintervalswe can generalize (see details in [10]) the concept of a fuzzy partition by taking basic functions that cover more than two consecutive subintervals. Consider an integer r 1 and 2r + 1 consecutive points (and consequently 2r subintervals) of P, x k r ; :::; x k ; :::; x k+r for all k = 1; 2; :::; n; to complete the notation, we extend the points to x 1 r < ::: < x 0 < a and b < x n+1 < ::: < x n+r . given by a pair (P; A (r) ) where P = fa = x 1 < x 2 < ::: < x n = bg is a decomposition of [a; b], and A (r) is a family of n + 2r 2 continuous, normal, convex fuzzy numbersr + 2; :::; n + r 1g such that a. for k = 1; 2; :::; n, Ak is a continuous fuzzy number with A

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“…The F-transform introduced by Perfilieva [25] has been studied and found useful in many applications in function approximation, image processing [22,27], numerical solutions of partial differential equations [36], data analysis [29] or neural network approaches [37]. The F-transform converts original data into weighted mean values where the weights are given by the basic functions which are membership functions to identify fuzzy sets.…”

Section: Introductionmentioning

confidence: 99%

A Novel Forecasting Method Based on F-Transform and Fuzzy Time Series

Lee

Jung

Lee

et al. 2017

Int. J. Fuzzy Syst.

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The main goal of time series analysis is to establish forecasting model based on past observations and to reduce forecasting error. To achieve these goals, the present paper proposes a new forecasting algorithm based on the fuzzy transform (F-transform) and the fuzzy logical relationships. First, the F-transform is performed based on partitioning of the universe, and the fuzzy logical relationships are employed to forecast. Two experimental applications are used to illustrate and verify the proposed algorithm. The accuracies are evaluated on the basis of average forecasting error percentage and index of agreement to compare the proposed algorithm with other existing methods.

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Fuzzy transform in the analysis of data

Cited by 116 publications

References 6 publications

On the relationship among F-transform, fuzzy rough set and fuzzy topology

On the relationship among F-transform, fuzzy rough set and fuzzy topology

Expectile Smoothing using F.transform

A Novel Forecasting Method Based on F-Transform and Fuzzy Time Series

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