Analysis of seasonal time series using fuzzy approach

Novák, Vilém; Štěpnička, Martin; Dvořák, Antonı́n; Perfilieva, Irina; Pavliska, Viktor; Vavříčková, Lenka

doi:10.1080/03081070903552965

Cited by 77 publications

(53 citation statements)

References 23 publications

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“…But, for our so-called linguistic approach originated by V. Novák [6] these questions were not adequately investigated. We were able to successfully apply our linguistic approach in analysis and forecasting of time series [7,8], decision making [9] or data mining [10]. We found out that this approach has distinct advantages in good interpretability, great robustness, foundations in a strong formal logical system etc.…”

Section: Introductionmentioning

confidence: 88%

New results on redundancies of fuzzy/linguistic IF-THEN rules

Štěpničková¹,

Štěpnička²,

Dvořák³

2013

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

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Section: Introductionmentioning

confidence: 88%

New results on redundancies of fuzzy/linguistic IF-THEN rules

Štěpničková¹,

Štěpnička²,

Dvořák³

2013

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

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“…In deriving the formula (6.3), we used max for "or" and min for "and". If we use sum for "or" and product for "and", we get F-transform instead of the formula (2); see, e.g., [11,26,27,29,30]. How to transform a membership function into a tuple: a reasonable requirement.…”

Section: For Each Number Xmentioning

confidence: 99%

50 Years of fuzzy: from discrete to continuous to – Where?

Kreinovich

Nguyen

Kosheleva

et al. 2015

IFS

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Abstract. While many objects and processes in the real world are discrete, from the computational viewpoint, discrete objects and processes are much more difficult to handle than continuous ones. As a result, a continuous approximation is often a useful way to describe discrete objects and processes. We show that the need for such an approximation explains many features of fuzzy techniques, and we speculate on to which promising future directions of fuzzy research this need can lead us.Keywords: fuzzy techniques, discrete, continuous, interval-valued fuzzy, complex-valued fuzzy, computing with words, dynamical fuzzy logic, chemical kinetics, non-additive measures, symmetry Fuzzy Techniques as an Easier-to-Compute Continuous Approximation for Difficult-to-Compute Discrete Objects and ProcessesDiscrete objects and processes are ubiquitous. Many real-life objects are processes are discrete. On the macro level, there is an abrupt transition in space between physical bodies, there is an abrupt transition in time when, e.g., a glass breaks or a person changes his/her opinion. On the micro level, matter consists of discrete atoms and molecules, with abrupt transitions between different states of an atom.Continuous problems are easier to compute. While discrete objects and processes are ubiquitous in nature, from the computational viewpoint, it is often much easier to handle continuous problems. This may sound * Corresponding author. E-mail: vladik@utep.edu.counter-intuitive, since intuitively, if we restrict our search or optimization to only integer values, the problem would become easier -but it is not. For example, in the continuous case, it is relatively easy to find a solution x 1 , . . . , x n to a system of linearmany known feasible algorithms for that), the problem becomes NP-hard (computationally intractable) if we only allow discrete values of x i ; see, e.g., [9,28].Similarly, in the continuous case, it is relatively easy to find the values x 1 , . . . , x n that minimize a given quadratic function f (x 1 , . . . , x n ): it is sufficient to solve the corresponding system of linear equations ∂f ∂x i = 0. However, optimization of quadratic functions for discrete inputs, e.g., for x i ∈ {0, 1}, is NPhard [9,28]. Continuous approximations of discrete objects and processes are ubiquitous in physics. Because dealing with discrete objects and processes is often computationally complicated, physicists often approximate discrete objects with continuous ones. For example, it is not feasible to describe the changes in atmosphere by tracing all 10 23 molecules, but approximate equations that describe the atmosphere as a continuous field leads to many useful weather predictions. Similar, a solid body -in effect, a collection of atoms -is well described by a continuous density field, and an atomic nucleus -a collection of protons and neutrons -is well described by a continuous (liquid) model; see, e.g., [8].Such approximations are also useful in analyzing social phenomena. For example, in analyzing how epidemics spread, ...

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“…In a time series analysis and forecast, the use of F-transform and inverse F-transform has been reported in many studies [22,23,[36][37][38]41]. In some studies, the F-transform was used to extract a low-frequency trend component [23,36,37], whereas it was used for the modeling of an autoregression function in [22].…”

Section: Introductionmentioning

confidence: 99%

“…Also, the inverse F-transform was used as a technical indicator in a stock market instead of the commonly used simple and exponential moving averages in other study [4]. Novak et al [23] have used inverse F-transform in combination with perception-based logical deduction, and Stepni ka et al [36,37] have provided forecasts of the future Ftransform components.…”

Section: Introductionmentioning

confidence: 99%

“…In some studies, the F-transform was used to extract a low-frequency trend component [23,36,37], whereas it was used for the modeling of an autoregression function in [22]. Also, the inverse F-transform was used as a technical indicator in a stock market instead of the commonly used simple and exponential moving averages in other study [4].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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Analysis of seasonal time series using fuzzy approach

Cited by 77 publications

References 23 publications

New results on redundancies of fuzzy/linguistic IF-THEN rules

New results on redundancies of fuzzy/linguistic IF-THEN rules

50 Years of fuzzy: from discrete to continuous to – Where?

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

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