The Experts below are selected from a list of 4929 Experts worldwide ranked by ideXlab platform
Vilém Novák - One of the best experts on this subject based on the ideXlab platform.
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filtering out high frequencies in time series using f transform with respect to raised cosine generalized uniform Fuzzy Partition
IEEE International Conference on Fuzzy Systems, 2015Co-Authors: Linh Nguyen, Vilém NovákAbstract:In this paper, we apply the F-transform technique with respect to raised cosine generalized uniform Fuzzy Partition to analysis of time series. We assume that the time series can be additively decomposed into trend-cycle, seasonal component and noise. We will prove that when constructing reasonably the Fuzzy Partition then the inverse F-transform of the time series provides a good approximation of its trend-cycle. Namely, the F-transform with respect to raised cosine generalized uniform Fuzzy Partition is able to eliminate completely the seasonal component and significantly reduce noise.
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FUZZ-IEEE - Filtering out high frequencies in time series using F-transform with respect to raised cosine generalized uniform Fuzzy Partition
2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2015Co-Authors: Linh Nguyen, Vilém NovákAbstract:In this paper, we apply the F-transform technique with respect to raised cosine generalized uniform Fuzzy Partition to analysis of time series. We assume that the time series can be additively decomposed into trend-cycle, seasonal component and noise. We will prove that when constructing reasonably the Fuzzy Partition then the inverse F-transform of the time series provides a good approximation of its trend-cycle. Namely, the F-transform with respect to raised cosine generalized uniform Fuzzy Partition is able to eliminate completely the seasonal component and significantly reduce noise.
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Necessary and sufficient conditions for generalized uniform Fuzzy Partitions
Fuzzy Sets and Systems, 2015Co-Authors: Michal Holcapek, Vilém Novák, Irina Perfilieva, Vladik KreinovichAbstract:Abstract The fundamental concept in the theory of Fuzzy transform (F-transform) is the Fuzzy Partition, which is a generalization of the classical concept of Partition. The original definition assumes that every two normal Fuzzy subsets in a Partition overlap in such a way that the sum of the membership degrees at each point is equal to 1. This condition can be generalized by relaxing the assumption of normality for Fuzzy sets. The result is a denser Fuzzy Partition that may improve the approximation properties and the smoothness of the inverse F-transform. A Fuzzy Partition with this property will be referred to as general. The problem is how a general Fuzzy Partition can be effectively constructed. If we use a generating function with special properties, then it is not immediately clear whether it defines a general Fuzzy Partition. In this paper, we find a necessary and sufficient condition that will enable the optimal generalized Fuzzy Partition to be designed more easily, which is important in various practical applications of the F-transform, for example, image processing, time series analysis, and solving differential equations with boundary conditions.
Linh Nguyen - One of the best experts on this subject based on the ideXlab platform.
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filtering out high frequencies in time series using f transform with respect to raised cosine generalized uniform Fuzzy Partition
IEEE International Conference on Fuzzy Systems, 2015Co-Authors: Linh Nguyen, Vilém NovákAbstract:In this paper, we apply the F-transform technique with respect to raised cosine generalized uniform Fuzzy Partition to analysis of time series. We assume that the time series can be additively decomposed into trend-cycle, seasonal component and noise. We will prove that when constructing reasonably the Fuzzy Partition then the inverse F-transform of the time series provides a good approximation of its trend-cycle. Namely, the F-transform with respect to raised cosine generalized uniform Fuzzy Partition is able to eliminate completely the seasonal component and significantly reduce noise.
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FUZZ-IEEE - Filtering out high frequencies in time series using F-transform with respect to raised cosine generalized uniform Fuzzy Partition
2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2015Co-Authors: Linh Nguyen, Vilém NovákAbstract:In this paper, we apply the F-transform technique with respect to raised cosine generalized uniform Fuzzy Partition to analysis of time series. We assume that the time series can be additively decomposed into trend-cycle, seasonal component and noise. We will prove that when constructing reasonably the Fuzzy Partition then the inverse F-transform of the time series provides a good approximation of its trend-cycle. Namely, the F-transform with respect to raised cosine generalized uniform Fuzzy Partition is able to eliminate completely the seasonal component and significantly reduce noise.
Vladik Kreinovich - One of the best experts on this subject based on the ideXlab platform.
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why use a Fuzzy Partition in f transform
Axioms, 2019Co-Authors: Vladik Kreinovich, Olga Kosheleva, Songsak SriboonchittaAbstract:In many application problems, F-transform algorithms are very efficient. In F-transform techniques, we replace the original signal or image with a finite number of weighted averages. The use of a weighted average can be naturally explained, e.g., by the fact that this is what we get anyway when we measure the signal. However, most successful applications of F-transform have an additional not-so-easy-to-explain feature: the Fuzzy Partition requirement that the sum of all the related weighting functions is a constant. In this paper, we show that this seemingly difficult-to-explain requirement can also be naturally explained in signal-measurement terms: namely, this requirement can be derived from the natural desire to have all the signal values at different moments of time estimated with the same accuracy. This explanation is the main contribution of this paper.
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adjoint Fuzzy Partition and generalized sampling theorem
International Conference Information Processing, 2016Co-Authors: Irina Perfilieva, Michal Holcapek, Vladik KreinovichAbstract:A new notion of adjoint Fuzzy Partition is introduced and the reconstruction of a function from its F-transform components is analyzed. An analogy with the Nyquist-Shannon-Kotelnikov sampling theorem is discussed.
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IPMU (2) - Adjoint Fuzzy Partition and Generalized Sampling Theorem
Information Processing and Management of Uncertainty in Knowledge-Based Systems, 2016Co-Authors: Irina Perfilieva, Michal Holcapek, Vladik KreinovichAbstract:A new notion of adjoint Fuzzy Partition is introduced and the reconstruction of a function from its F-transform components is analyzed. An analogy with the Nyquist-Shannon-Kotelnikov sampling theorem is discussed.
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Necessary and sufficient conditions for generalized uniform Fuzzy Partitions
Fuzzy Sets and Systems, 2015Co-Authors: Michal Holcapek, Vilém Novák, Irina Perfilieva, Vladik KreinovichAbstract:Abstract The fundamental concept in the theory of Fuzzy transform (F-transform) is the Fuzzy Partition, which is a generalization of the classical concept of Partition. The original definition assumes that every two normal Fuzzy subsets in a Partition overlap in such a way that the sum of the membership degrees at each point is equal to 1. This condition can be generalized by relaxing the assumption of normality for Fuzzy sets. The result is a denser Fuzzy Partition that may improve the approximation properties and the smoothness of the inverse F-transform. A Fuzzy Partition with this property will be referred to as general. The problem is how a general Fuzzy Partition can be effectively constructed. If we use a generating function with special properties, then it is not immediately clear whether it defines a general Fuzzy Partition. In this paper, we find a necessary and sufficient condition that will enable the optimal generalized Fuzzy Partition to be designed more easily, which is important in various practical applications of the F-transform, for example, image processing, time series analysis, and solving differential equations with boundary conditions.
Hu Chunchun - One of the best experts on this subject based on the ideXlab platform.
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Cluster Validity Index Based on Measure of Fuzzy Partition
Computer Engineering, 2007Co-Authors: Hu ChunchunAbstract:Cluster validity index is used to evaluate the validity of clustering.Anew cluster validity index is proposed to identify the optimal Fuzzy Partition according to the basic properties of clustering.The index exploits two important evaluation factors: the measure of Fuzzy Partition and information entropy.The first factor is used to evaluate the compress within a cluster and the separation between clusters,and the second is to measure the uncertainty of the Partition result.The experimental results indicate that the index is effective and efficient for evaluating the result of Fuzzy clustering.Especially,for the spatial data,the index can correctly identify the optimal clustering number and is not sensitive to the weighting exponent.
Jiu-lun Fan - One of the best experts on this subject based on the ideXlab platform.
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Image segmentation based on weak Fuzzy Partition entropy
Neurocomputing, 2015Co-Authors: Xiao-bin Zhi, Jiu-lun FanAbstract:Fuzzy Partition entropy-based method is an effective way for image segmentation. In this paper a segmentation method based on a weak Fuzzy Partition is presented. Firstly, we propose a method to construct generalized Fuzzy complement, and moreover construct a generalized Fuzzy complement operator which has a nice property for parameter optimization in real application. Then, a one-dimensional (1D) weak Fuzzy Partition, a two-dimensional (2D) weak Fuzzy Partition being obtained by a Cartesian product of two 1D Fuzzy Partitions, are defined using the proposed generalized Fuzzy complement. With these concepts, a weak Fuzzy Partition entropy-based image segmentation method is proposed. The method is described in the 1D and 2D cases by modeling the 1D and 2D histograms. The 2D approach allows us to ensure a spatial regularity of the Fuzzy classification. Finally, a nested optimization method is developed, based on an improved uniformity measure, to search for the optimal threshold in the image segmentation method. Empirical results show that the proposed weak Fuzzy Partition entropy-based method is capable of achieving better segmentation results than several state-of-the-art methods that are based on or not based on Fuzzy entropy. The proposed 2D weak Fuzzy Partition entropy-based method is especially effective for noisy images.
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parameter selection for suppressed Fuzzy c means clustering algorithm based on Fuzzy Partition entropy
Fuzzy Systems and Knowledge Discovery, 2014Co-Authors: Jiu-lun FanAbstract:Suppressed Fuzzy c-means (S-FCM) clustering algorithm with the intention of combining the higher speed of hard c-means clustering algorithm and the better classification performance of Fuzzy c-means clustering algorithm had been studied by many researchers and applied in many fields. In this algorithm, the parameter selection is very important on the algorithm performance. Huang proposed a modified S-FCM, named as MS-FCM, to determine the parameter α with type-driven learning. α is updated each iteration and successful used in MRI segmentation. In this paper, we give another method to select the parameter α based on the Fuzzy Partition entropy. Numerical examples will serve to illustrate the effectiveness of proposed algorithm.
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three level image segmentation based on maximum Fuzzy Partition entropy of 2 d histogram and quantum genetic algorithm
International Conference on Intelligent Computing, 2008Co-Authors: Jiu-lun FanAbstract:A method is presented for three-level image segmentation through maximizing the Fuzzy Partition entropy of two-dimensional histogram. Two groups, each including three member functions, namely Z-function, i¾?-function and S-function, are used for Fuzzy division of two-dimensional histogram to get nine Fuzzy sets. And the nine Fuzzy sets are classified to three parts, corresponding to dark, gray and white part of the image, respectively, while a Fuzzy Partition is obtained for the two-dimensional space. Then a Fuzzy Partition entropy is defined based on multi-dimensional Fuzzy Partition and entropy theory. The parameters of the six membership functions can be determined by maximizing Fuzzy Partition entropy of two-dimensional histogram and the procedure for finding the optimal combination of all the Fuzzy parameters is implemented by quantum genetic algorithm with an appropriate coding method. The experiment results show that the proposed method gives better performance than onedimensional three-level thresholding method under noise case.
