Analysis of Periodical Time Series Using Soft Computing Methods

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

doi:10.1142/9789812799470_0009

Cited by 20 publications

(13 citation statements)

References 3 publications

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“…Some of the methods are available as a software package "lfl" (Linguistic Fuzzy Logic) [19] for the open-source R statistical environment [20]. The approach of this paper puts together results of several papers ( [21,22,23,24,25,26]). The primary objective of this paper is to put together GUHA method, the theory of evaluative linguistic expressions and the theory of intermediate quantifiers and to bring new results from natural data using acquired information in sentences of natural language.…”

Section: Fuzzy Natural Logicmentioning

confidence: 99%

Linguistic Characterization of Natural Data by Applying Intermediate Quantifiers on Fuzzy Association Rules

Murinová¹,

Burda²

2017

The Oxford Journal of Intelligent Decision and Data Science

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The paper aims at applying fuzzy natural logic together with the Fuzzy GUHA method to analyse and linguistically characterise scientific data. Fuzzy GUHA is a tool for extracting linguistic association rules from data. Obtained associations are IF-THEN rules composed of evaluative linguistic expressions, which allow the quantities to be characterized with vague linguistic terms such as "very small", "big", "medium" etc. Originally, fuzzy GUHA provides several numerical indices of rule quality, which may not be easily understandable for domain experts that are not familiar with GUHA association rules. Therefore, we show in this paper that the theory of intermediate quantifiers (a constituent of fuzzy natural logic) can be applied to the results in an automatic manner in order to obtain natural linguistic summarization. We also present an idea of how the theory of generalized Aristotles's syllogisms can be used for a detailed data analysis. We also open the possibility to use fuzzy partial logic for cases where some data is missing or undefined.

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Section: Fuzzy Natural Logicmentioning

confidence: 99%

Linguistic Characterization of Natural Data by Applying Intermediate Quantifiers on Fuzzy Association Rules

Murinová¹,

Burda²

2017

The Oxford Journal of Intelligent Decision and Data Science

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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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“…Thus, we arrive at the following definition; see, e.g., [1], [4], [5], [6], [7]: Definition 1. Let t 0 and h > 0 be real numbers, let n > 0 be an integer, and let t i …”

Section: F-transforms: Remindermentioning

confidence: 99%

“…It should be mentioned that while our motivation for F-transform came from compression, F-transforms are useful beyond compression. For example, when we first perform F-transform and then inverse F-transform, we also get rid of the high-frequency noise, and so, F-transforms are also very useful for de-noising and smoothing; see, e.g., [1], [4], [5], [6], [7].…”

Section: Commentmentioning

confidence: 99%

Why inverse F-transform? A compression-based explanation

Kreinovich

Perfilieva

Novák

2013

2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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Abstract-In many practical situations, e.g., in signal processing, image processing, analysis of temporal data, it is very useful to use fuzzy (F-) transforms. In an F-transform, we first replace a function x(t) by a few local averages (this is called forward Ftransform), and then reconstruct the original function from these averages (this is called inverse F-transform). While the formula for the forward F-transform makes perfect intuitive sense, the formula for the inverse F-transform seems, at first glance, somewhat counter-intuitive. On the other hand, its empirical success shows that this formula must have a good justification. In this paper, we provide such a justification -a justification which is based on formulating a reasonable compression-based criterion. I. FORMULATION OF THE PROBLEMMain problem. In many real-life situations, fuzzy transform (F-transform, for short) leads to a good quality compression of the original signals, images, etc.How can we explain this empirical fact? Approximation problems are well-known and well-studied in numerical mathematics, so, at first glance, we should simply use the corresponding well-developed optimization criteria and confirm that F-transform is indeed better according to these criteria. Surprisingly, while F-transform is often empirically better, the existing theoretical criteria select other approximation methods as much better ones.This discrepancy between empirical evidence and the existing theoretical criteria shows that these criteria are not fully adequate for comparing real-life compression results.What we do in this paper. In this paper, we formulate a more adequate theoretical criterion, and we show that -in accordance with the empirical data -that this criterion indeed leads to F-transform.The structure of the paper. We start with a detailed description of F-transforms in Section 2. This section contains not only the formal definitions, it also contains motivations for these definitions. In Section 3, we explain that with respect to the standard optimization criteria from numerical analysis, the F-transform formulas are not optimal. In Section 4, we present a general definition of the inverse transform, a definition which includes both F-transform and the traditional numerical approximations as particular cases. Finally, in Section 5, we derive the new criterion for selecting compression techniques, and we show that this new criterion leads to F-transform. The results are summarized in the Conclusions section. II. F-TRANSFORMS: REMINDERData compression: one of the problems for which Ftransforms were invented. In many practical situations, we need to compress the data. For example, we have records describing how a certain physical characteristic x (e.g., temperature) changes with time. Sometimes, it takes too much space to store all this information; sometimes, it takes too much computation time to process all this information. In all these situations, we need to compress the data, i.e., to replace the original values x(t) corresponding to different mome...

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Analysis of Periodical Time Series Using Soft Computing Methods

Cited by 20 publications

References 3 publications

Linguistic Characterization of Natural Data by Applying Intermediate Quantifiers on Fuzzy Association Rules

Linguistic Characterization of Natural Data by Applying Intermediate Quantifiers on Fuzzy Association Rules

Computing with Words: Towards a New Tuple-Based Formalization

Why inverse F-transform? A compression-based explanation

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