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Yuzhong Zhang - One of the best experts on this subject based on the ideXlab platform.

  • Entropy similarity Measure of interval valued intuitionistic fuzzy sets and their applications
    Information Sciences, 2011
    Co-Authors: Cuiping Wei, Pei Wang, Yuzhong Zhang
    Abstract:

    In this paper we propose an Entropy Measure for interval-valued intuitionistic fuzzy sets, which generalizes three Entropy Measures defined independently by Szmidt, Wang and Huang, for intuitionistic fuzzy sets. We also give an approach to construct similarity Measures using Entropy Measures for interval-valued intuitionistic fuzzy sets. In particular, the proposed Entropy Measure for interval-valued intuitionistic fuzzy sets can yield a similarity Measure. Several illustrative examples are given to demonstrate the practicality and effectiveness of the proposed formulas. We apply the similarity Measure to solve problems on pattern recognitions, multi-criteria fuzzy decision making and medical diagnosis.

Bernadette Dorizzi - One of the best experts on this subject based on the ideXlab platform.

  • A novel criterion for writer enrolment based on a time-normalized signature sample Entropy Measure
    EURASIP Journal on Advances in Signal Processing, 2009
    Co-Authors: Sonia Garcia-salicetti, Nesma Houmani, Bernadette Dorizzi
    Abstract:

    This paper proposes a novel criterion for an improved writer enrolment based on an Entropy Measure for online genuine signatures. As online signature is a temporal signal, we Measure the time-normalized Entropy of each genuine signature, namely, its average Entropy per second. Entropy is computed locally, on portions of a genuine signature, based on local density estimation by a Client-Hidden Markov Model. The average time-normalized Entropy computed on a set of genuine signatures allows then categorizing writers in an unsupervised way, using a K-Means algorithm. Linearly separable and visually coherent classes of writers are obtained on MCYT-100 database and on a subset of BioSecure DS2 containing 104 persons (DS2-104). These categories can be analyzed in terms of variability and complexity Measures that we have defined in this work. Moreover, as each category can be associated with a signature prototype inherited from the K-Means procedure, we can generalize the writer categorization process on the large subset DS2-382 from the same DS2 database, containing 382 persons. Performance assessment shows that one category of signatures is significantly more reliable in the recognition phase, and given the fact that our categorization can be used online, we propose a novel criterion for enhanced writer enrolment

  • A novel personal Entropy Measure confronted to online signature verification systems' performance
    2008
    Co-Authors: Nesma Houmani, Sonia Garcia-salicetti, Bernadette Dorizzi
    Abstract:

    In this paper, we study the relation between a novel personal Entropy Measure for online signatures, based on local density estimation by a Hidden Markov Model, and the performance of several state-of-the-art classifiers for online signature verification. We show that there is a clear relation between such Entropy Measure of a person’s signature and behavior of the classifier. We carry out this study on a Dynamic Time Warping classifier, a Gaussian Mixture Model and a Hidden Markov Model as well. Signatures were split by the K-Means algorithm in three categories which are coherent across four different databases of around 100 persons each: BIOMET, MCYT-100, BioSecure data subsets DS2 and DS3. We studied the impact of such categories on classifier’s performance with a larger signature data subset of DS3, of 430 persons

  • A Novel Personal Entropy Measure confronted with Online Signature Verification Systems' Performance
    2008 IEEE Second International Conference on Biometrics: Theory Applications and Systems, 2008
    Co-Authors: Nesma Houmani, Sonia Garcia-salicetti, Bernadette Dorizzi
    Abstract:

    In this paper, we study the relationship between a novel personal Entropy Measure for online signatures and the performance of several state-of-the-art classifiers. The Entropy Measure is based on local density estimation by a hidden Markov model. We show that there is a clear relationship between such Entropy Measure of a person's signature and the behavior of the classifier. We carry out this study on a dynamic time warping classifier, a Gaussian mixture model and a hidden Markov model as well. It is worth noticing that the HMM classifier differs from the HMM used for Entropy computation. Signatures were split into three categories according to their Entropy value. These categories are coherent across four different databases of around 100 persons each: BIOMET, MCYT-100, BioSecure data subsets DS2 and DS3. We studied the impact of such categories on classifier's performance with a larger signature data subset of DS3, of 430 persons.

  • A client-Entropy Measure for On-line Signatures
    2008 Biometrics Symposium, 2008
    Co-Authors: S.g. Salicetti, Nesma Houmani, Bernadette Dorizzi
    Abstract:

    In this article, we propose an original way to characterize information content in online signatures through a client-Entropy Measure based on local density estimation by a hidden Markov model. We show that this Measure can be used to categorize signatures in visually coherent classes that can be related to complexity and variability criteria. Besides, the generated categories are coherent across four different databases: BIOMET, MCYT-100, BioSecure data subsets DS2 and DS3. This Measure allows a comparison of databases in terms of clientspsila signatures according to their information content.

Cuiping Wei - One of the best experts on this subject based on the ideXlab platform.

  • Entropy similarity Measure of interval valued intuitionistic fuzzy sets and their applications
    Information Sciences, 2011
    Co-Authors: Cuiping Wei, Pei Wang, Yuzhong Zhang
    Abstract:

    In this paper we propose an Entropy Measure for interval-valued intuitionistic fuzzy sets, which generalizes three Entropy Measures defined independently by Szmidt, Wang and Huang, for intuitionistic fuzzy sets. We also give an approach to construct similarity Measures using Entropy Measures for interval-valued intuitionistic fuzzy sets. In particular, the proposed Entropy Measure for interval-valued intuitionistic fuzzy sets can yield a similarity Measure. Several illustrative examples are given to demonstrate the practicality and effectiveness of the proposed formulas. We apply the similarity Measure to solve problems on pattern recognitions, multi-criteria fuzzy decision making and medical diagnosis.

Wen-jing Tian - One of the best experts on this subject based on the ideXlab platform.

  • Entropy Measure of Generating Random Rough Surface for Numerical Simulation of Wave Scattering
    IEEE Transactions on Geoscience and Remote Sensing, 2020
    Co-Authors: Rui Jiang, Kun-shan Chen, Wen-jing Tian
    Abstract:

    Numerical simulation of random rough surface finds wide applications in scientific disciplines, e.g., radar remote sensing of terrain and sea. In scattering simulation of rough surface, not only energy conservation must be ensured, but also, perhaps equally important, the surface inherent properties must be preserved. However, the proper choice of surface and grid sizes that are statistically representative poses a problematic issue. This study applied the Entropy Measure to determine such parameter settings by examining the relative error of sample Entropy associated with roughness parameters and by noticing the fact that a rough surface with certain roughness parameters, including power spectrum density function, must have unique sample Entropy. It is found that if the two criteria are met, proper choice of surface length and grid size is attainable to warrant minimum uncertainties of rough surfaces and maximum information content for different roughness spectra density functions under different correlation lengths. The feasibility and superiority of the proposed Entropy-based method are validated in terms of minimum error of roughness parameters and also the energy conservation in bistatic scattering coefficients of rough surfaces generated using obtained simulation parameters.

Eitan Tadmor - One of the best experts on this subject based on the ideXlab platform.

  • Construction of Approximate Entropy Measure-Valued Solutions for Hyperbolic Systems of Conservation Laws
    Foundations of Computational Mathematics, 2017
    Co-Authors: Ulrik S. Fjordholm, Roger Käppeli, Siddhartha Mishra, Eitan Tadmor
    Abstract:

    Entropy solutions have been widely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in De Lellis and Székelyhidi Jr (Ann Math 170(3):1417–1436, 2009 ) and Chiodaroli et al. ( 2013 ) have demonstrated that Entropy solutions may not be unique. In this paper, we present numerical evidence that state-of-the-art numerical schemes need not converge to an Entropy solution of systems of conservation laws as the mesh is refined. Combining these two facts, we argue that Entropy solutions may not be suitable as a solution framework for systems of conservation laws, particularly in several space dimensions. We advocate Entropy Measure-valued solutions , first proposed by DiPerna, as the appropriate solution paradigm for systems of conservation laws. To this end, we present a detailed numerical procedure which constructs stable approximations to Entropy Measure-valued solutions, and provide sufficient conditions that guarantee that these approximations converge to an Entropy Measure-valued solution as the mesh is refined, thus providing a viable numerical framework for systems of conservation laws in several space dimensions. A large number of numerical experiments that illustrate the proposed paradigm are presented and are utilized to examine several interesting properties of the computed Entropy Measure-valued solutions.

  • construction of approximate Entropy Measure valued solutions for hyperbolic systems of conservation laws
    Foundations of Computational Mathematics, 2017
    Co-Authors: Ulrik S. Fjordholm, Roger Käppeli, Siddhartha Mishra, Eitan Tadmor
    Abstract:

    Entropy solutions have been widely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in De Lellis and Szekelyhidi Jr (Ann Math 170(3):1417---1436, 2009) and Chiodaroli et al. (2013) have demonstrated that Entropy solutions may not be unique. In this paper, we present numerical evidence that state-of-the-art numerical schemes need not converge to an Entropy solution of systems of conservation laws as the mesh is refined. Combining these two facts, we argue that Entropy solutions may not be suitable as a solution framework for systems of conservation laws, particularly in several space dimensions. We advocate Entropy Measure-valued solutions, first proposed by DiPerna, as the appropriate solution paradigm for systems of conservation laws. To this end, we present a detailed numerical procedure which constructs stable approximations to Entropy Measure-valued solutions, and provide sufficient conditions that guarantee that these approximations converge to an Entropy Measure-valued solution as the mesh is refined, thus providing a viable numerical framework for systems of conservation laws in several space dimensions. A large number of numerical experiments that illustrate the proposed paradigm are presented and are utilized to examine several interesting properties of the computed Entropy Measure-valued solutions.

  • Construction of approximate Entropy Measure valued solutions for hyperbolic systems of conservation laws
    Foundations of Computational Mathematics, 2015
    Co-Authors: Ulrik S. Fjordholm, Roger Käppeli, Siddhartha Mishra, Eitan Tadmor
    Abstract:

    Entropy solutions have been widely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in \cite{CDL1,CDL2} have demonstrated that Entropy solutions may not be unique. In this paper, we present numerical evidence that demonstrates that state of the art numerical schemes \emph{may not} necessarily converge to an Entropy solution of systems of conservation laws as the mesh is refined. Combining these two facts, we argue that Entropy solutions may not be suitable as a solution framework for systems of conservation laws, particularly in several space dimensions. Furthermore, we propose a more general notion, that of \emph{Entropy Measure valued solutions}, as an appropriate solution paradigm for systems of conservation laws. To this end, we present a detailed numerical procedure, which constructs stable approximations to Entropy Measure valued solutions and provide sufficient conditions that guarantee that these approximations converge to an Entropy Measure valued solution as the mesh is refined, thus providing a viable numerical framework for systems of conservation laws in several space dimensions. A large number of numerical experiments that illustrate the proposed schemes are presented and are utilized to examine several interesting properties of the computed Entropy Measure valued solutions.