Analysis and prediction of time series using fuzzy transform

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

doi:10.1109/ijcnn.2008.4634355

Cited by 26 publications

(16 citation statements)

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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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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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“…The transformation defined in this Section uses a different approach and is completely distinct from the one with resembling name introduced and studied in [3], [10][11][12][13][14], although the application fields of these transforms may overlap.…”

Section: Definitions Properties and Examples Of Fuzzy Transformsmentioning

confidence: 99%

Coordinate Fuzzy Transforms and Fuzzy Tent Maps – Properties and Applications

Teodorescu¹

2015

SIC

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“…In deriving the formula (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., [1], [4], [5], [6], [7].…”

Section: A Seemingly Natural Idea and Its Limitationsmentioning

confidence: 99%

Computing with Words: Towards a New Tuple-Based Formalization

Kosheleva

Kreinovich

Garcia

et al. 2013

2013 IEEE International Conference on Systems, Man, and Cybernetics

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Abstract-An expert opinion describes his or her opinion about a quantity by using imprecise ("fuzzy") words from a natural language, such as "small", "medium", "large", etc. Each of these words provides a rather crude description of the corresponding quantity. A natural way to refine this description is to assign degrees to which the observed quantity fits each of the selected words. For example, an expert can say that the value is reasonable small, but to some extent it is medium. In this refined description, we represent each quantity by a tuple of the corresponding degrees.Once we have such a tuple-based information about several quantities x1, . . . , xm, and we know that another quantity y is related to xi by a known relation y = f (x1, . . . , xm), it is desirable to come up with a resulting tuple-based description of y. In this paper, we describe why a seemingly natural idea for computing such a tuple does not work, and we show how to modify this idea so that it can be used.

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Analysis and prediction of time series using fuzzy transform

Abstract: A new methodology for forecasting of time series is proposed. It is based on combination of two techniques: fuzzy transform and perception-based logical deduction on the basis of learned linguistic description.

Cited by 26 publications

References 11 publications

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

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

Coordinate Fuzzy Transforms and Fuzzy Tent Maps – Properties and Applications

Computing with Words: Towards a New Tuple-Based Formalization

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