Towards a higher degree F-transform

Perfilieva, Irina; Daňková, Martina; Bede, Barnabás

doi:10.1016/j.fss.2010.11.002

Cited by 125 publications

(76 citation statements)

References 5 publications

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“…We consider D = X × Y as a common domain of all L-valued functions and shown that the lattice F-transform for functions in single variable can naturally be extended to that in two variables. The concept of higher degree F-transform has already been introduced in [20] by taking the function f as an orthogonal zero and first degree polynomials. We will try to study the higher degree lattice F-transform for functions in multiple variables in the near future.…”

Section: Resultsmentioning

confidence: 99%

Lattice $F$-transform for functions in two variables

Singh¹,

Tiwari²

2016

Journal of Fuzzy Set Valued Analysis

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Section: Resultsmentioning

confidence: 99%

Lattice $F$-transform for functions in two variables

Singh¹,

Tiwari²

2016

Journal of Fuzzy Set Valued Analysis

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“…This generalization has been in detail described in 23 . Besides better approximation properties, it enables us to estimate also derivatives of the given function f as average values over wider area.…”

Section: F 1 -Transformmentioning

confidence: 99%

“…8, Supplement 1 (2015), [15][16][17][18][19][20][21][22][23][24][25][26][27][28] Co-published by Atlantis Press and Taylor & Francis Copyright: the authorsnetworks or genetic algorithms (cf. 11 and the citations therein).…”

Section: Introductionmentioning

confidence: 99%

Forecasting Direction of Trend of a Group of Analogous Time Series Using F-Transform and Fuzzy Natural Logic

Novák¹,

Perfilieva²

2015

IJCIS

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We present an idea to group time series according to similarity of their local trends and to predict future direction of the trend of all of them on the basis of forecast of only one representative. First, we assign to each time series an adjoint one, which consists of a sequence of the F 1 -transform components. Then, they are grouped together according to their similarity, a principal time series is selected in each group and its future course is forecasted. Finally, directions of trends of the other time series from the same group are computed using special methods of fuzzy natural logic.

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“…The F m -transform of a higher degree m ≥ 1 was introduced in [5]. In this section we give a short description of the F 1 -transform of functions of one variable.…”

Section: F 1 -Transform Of Functions Of One Variablementioning

confidence: 99%

“…Generalization of the ordinary F-transform to the F-transform of a higher degree in the case of functions of one variable was introduced in [5]. Many interesting properties of the F-transform of a higher degree have been proved there, and among others, a property of approximation of the first derivative of the original function.…”

Section: Introductionmentioning

confidence: 99%