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Gilles Mauris - One of the best experts on this subject based on the ideXlab platform.
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image change detection by Possibility Distribution dissemblance
IEEE International Conference on Fuzzy Systems, 2017Co-Authors: Charles Lesniewskachoquet, Gilles Mauris, Abdourrahmane Atto, Grégoire MercierAbstract:In this paper we present a new similarity measure between Possibility Distributions based on the Kullback-Leibler (KL) divergence in the domain of real numbers. The Possibility Distributions are obtained thanks to the DFMP probability-Possibility transformation [1] lying on the principle that a Possibility measure can encode a family of probability measures. We consider here two particular Possibility Distributions built from parameter estimation of the Weibull and Rayleigh probability laws. The analytical expression of the KL divergence for the two considered Possibility Distributions are given, allowing a simple computation which depends on the parameters of the Possibility Distribution obtained. This new similarity measure is compared to the existing KL divergence for probability Distributions in a context of change detection over simulated images as they provide a ground-truth of the changes required to evaluate the rate of true detection against false alarm.
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Image Change Detection by Possibility Distribution Dissemblance
2017Co-Authors: Charles Lesniewska-choquet, Gilles Mauris, Abdourrahmane Atto, Grégoire MercierAbstract:In this paper we present a new similarity measure between Possibility Distributions based on the Kullback-Leilbler divergence in the domain of real numbers. The Possibility Distributions are obtained thanks to a previously proposed probability-Possibility transformation lying on the principle that a Possibility measure can encode a family of probability measures. We consider here two particular Possibility Distributions build from parameter estimation of the Weibull and Rayleigh probability laws. The analytical expression of the KL divergence for the two considered Possibility Distributions are given, allowing a simple computation which depends on the parameters of the Possibility Distribution obtained. This new similarity measure is compared to the existing KL divergence for probability Distributions in a context of change detection over simulated images as they provide a ground-truth of the changes required to evaluate the rate of true detection against false alarm.
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FUZZ-IEEE - Image change detection by Possibility Distribution dissemblance
2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2017Co-Authors: Charles Lesniewska-choquet, Gilles Mauris, Abdourrahmane Atto, Grégoire MercierAbstract:In this paper we present a new similarity measure between Possibility Distributions based on the Kullback-Leibler (KL) divergence in the domain of real numbers. The Possibility Distributions are obtained thanks to the DFMP probability-Possibility transformation [1] lying on the principle that a Possibility measure can encode a family of probability measures. We consider here two particular Possibility Distributions built from parameter estimation of the Weibull and Rayleigh probability laws. The analytical expression of the KL divergence for the two considered Possibility Distributions are given, allowing a simple computation which depends on the parameters of the Possibility Distribution obtained. This new similarity measure is compared to the existing KL divergence for probability Distributions in a context of change detection over simulated images as they provide a ground-truth of the changes required to evaluate the rate of true detection against false alarm.
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Possibility transformation of the sum of two symmetric unimodal independent/comonotone random variables
2013Co-Authors: Gilles MaurisAbstract:The paper extends author's previous works on a probability/Possibility transformation based on a maximum specificity principle to the case of the sum of two identical unimodal symmetric random variables. This transformation requires the knowledge of the dependency relationship between the two added variables. In fact, the comonotone case is closely related to the Zadeh's extension principle. It often leads to the worst case in terms of specificity of the corresponding Possibility Distribution, but it may arise that the independent case is worse than the comonotone case, e.g. for symmetric Pareto probability Distributions. When no knowledge about the dependence is available, a least specific pos-sibility Distribution can be obtained from Fréchet bounds.
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Possibility Distributions: A unified representation of usual direct-probability-based parameter estimation methods
International Journal of Approximate Reasoning, 2011Co-Authors: Gilles MaurisAbstract:The paper presents a Possibility theory based formulation of one-parameter estimation that unifies some usual direct probability formulations. Point and confidence interval estimation are expressed in a single theoretical formulation and incorporated into estimators of a generic form: a Possibility Distribution. New relationships between continuous Possibility Distribution and probability concepts are established. The notion of specificity ordering of a Possibility Distribution, corresponding to fuzzy subsets inclusion, is then used for comparing the efficiency of different estimators for the case of data points coming from a symmetric probability Distribution. The usefulness of the approach is illustrated on common mean and median estimators from identical independent data sample of different size and of different common symmetric continuous probability Distributions.
Hideo Tanaka - One of the best experts on this subject based on the ideXlab platform.
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Upper and Lower Possibility Distributions with Rough Set Concepts
Rough Set Theory and Granular Computing, 2003Co-Authors: Peijun Guo, Hideo TanakaAbstract:In this paper, the dual Possibility Distributions, called upper and lower Possibility Distributions, initially proposed by Tanaka and Guo are redefined with considering the concept of rough sets to characterize the intrinsic uncertainty of human judgment. These two Possibility Distributions are identified from the given data to reflect twoextreme opinions on a specified event. The upper Possibility Distribution can be regarded as an optimistic viewpoint and the lower Distribution as a pessimistic one in the sense that the upper Possibility Distribution always gives a higher Possibility grade than the lower one. The similarities between the concepts of upper and lower approximations in rough sets theory and the concepts of upper and lower Possibility Distributions in Possibility theory are shown in detail.
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JSAI Workshops - Identifying Upper and Lower Possibility Distributions with Rough Set Concept
New Frontiers in Artificial Intelligence, 2001Co-Authors: Peijun Guo, Hideo TanakaAbstract:In this paper, from upper and lower directions the upper and lower Possibility Distributions are identified to approximate the given Possibility grades, which is regarded as the expert’s knowledge. The upper Possibility Distribution reflects the optimistic viewpoint of the expert and the lower Possibility Distribution reflects pessimistic one. The similarities between dual Possibility Distributions and upper and lower approximations in rough sets theory are investigated. It is obvious that they have homogenous structures.
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Possibility Distributions of fuzzy decision variables obtained from possibilistic linear programming problems
Fuzzy Sets and Systems, 2000Co-Authors: Hideo Tanaka, Peijun Guo, Hans-jürgen ZimmermannAbstract:Abstract In this paper, several kinds of Possibility Distributions of fuzzy variables are studied in possibilistic linear programming problems to reflect the inherent fuzziness in fuzzy decision problems. Interval and triangular Possibility Distributions are used to express the non-interactive cases between the fuzzy decision variables, and exponential Possibility Distributions are used to represent the interrelated cases. Possibilistic linear programming problems based on exponential Possibility Distributions become non-linear optimization problems. In order to solve optimization problems easily, algorithms for obtaining center vectors and Distribution matrices in sequence are proposed. By the proposed algorithms, the Possibility Distribution of fuzzy decision variables can be obtained.
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Portfolio selection based on upper and lower exponential Possibility Distributions
European Journal of Operational Research, 1999Co-Authors: Hideo Tanaka, Peijun GuoAbstract:In this paper, two kinds of Possibility Distributions, namely, upper and lower Possibility Distributions are identified to reflect experts' knowledge in portfolio selection problems. Portfolio selection models based on these two kinds of Distributions are formulated by quadratic programming problems. It can be said that a portfolio return based on the lower Possibility Distribution has smaller Possibility spread than the one on the upper Possibility Distribution. In addition, a Possibility risk can be defined as an interval given by the spreads of the portfolio returns from the upper and the lower Possibility Distributions to reflect the uncertainty in real investment problems. A numerical example of a portfolio selection problem is given to illustrate our proposed approaches.
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Theory and Methodology Portfolio selection based on upper and lower exponential Possibility Distributions
1999Co-Authors: Hideo Tanaka, Peijun GuoAbstract:In this paper, two kinds of Possibility Distributions, namely, upper and lower Possibility Distributions are identified to reflect experts’ knowledge in portfolio selection problems. Portfolio selection models based on these two kinds of Distributions are formulated by quadratic programming problems. It can be said that a portfolio return based on the lower Possibility Distribution has smaller Possibility spread than the one on the upper Possibility Distribution. In addition, a Possibility risk can be defined as an interval given by the spreads of the portfolio returns from the upper and the lower Possibility Distributions to reflect the uncertainty in real investment problems. A numerical example of a portfolio selection problem is given to illustrate our proposed approaches. ” 1999 Elsevier Science B.V. All rights reserved.
Peijun Guo - One of the best experts on this subject based on the ideXlab platform.
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Upper and Lower Possibility Distributions with Rough Set Concepts
Rough Set Theory and Granular Computing, 2003Co-Authors: Peijun Guo, Hideo TanakaAbstract:In this paper, the dual Possibility Distributions, called upper and lower Possibility Distributions, initially proposed by Tanaka and Guo are redefined with considering the concept of rough sets to characterize the intrinsic uncertainty of human judgment. These two Possibility Distributions are identified from the given data to reflect twoextreme opinions on a specified event. The upper Possibility Distribution can be regarded as an optimistic viewpoint and the lower Distribution as a pessimistic one in the sense that the upper Possibility Distribution always gives a higher Possibility grade than the lower one. The similarities between the concepts of upper and lower approximations in rough sets theory and the concepts of upper and lower Possibility Distributions in Possibility theory are shown in detail.
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JSAI Workshops - Identifying Upper and Lower Possibility Distributions with Rough Set Concept
New Frontiers in Artificial Intelligence, 2001Co-Authors: Peijun Guo, Hideo TanakaAbstract:In this paper, from upper and lower directions the upper and lower Possibility Distributions are identified to approximate the given Possibility grades, which is regarded as the expert’s knowledge. The upper Possibility Distribution reflects the optimistic viewpoint of the expert and the lower Possibility Distribution reflects pessimistic one. The similarities between dual Possibility Distributions and upper and lower approximations in rough sets theory are investigated. It is obvious that they have homogenous structures.
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Possibility Distributions of fuzzy decision variables obtained from possibilistic linear programming problems
Fuzzy Sets and Systems, 2000Co-Authors: Hideo Tanaka, Peijun Guo, Hans-jürgen ZimmermannAbstract:Abstract In this paper, several kinds of Possibility Distributions of fuzzy variables are studied in possibilistic linear programming problems to reflect the inherent fuzziness in fuzzy decision problems. Interval and triangular Possibility Distributions are used to express the non-interactive cases between the fuzzy decision variables, and exponential Possibility Distributions are used to represent the interrelated cases. Possibilistic linear programming problems based on exponential Possibility Distributions become non-linear optimization problems. In order to solve optimization problems easily, algorithms for obtaining center vectors and Distribution matrices in sequence are proposed. By the proposed algorithms, the Possibility Distribution of fuzzy decision variables can be obtained.
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Portfolio selection based on upper and lower exponential Possibility Distributions
European Journal of Operational Research, 1999Co-Authors: Hideo Tanaka, Peijun GuoAbstract:In this paper, two kinds of Possibility Distributions, namely, upper and lower Possibility Distributions are identified to reflect experts' knowledge in portfolio selection problems. Portfolio selection models based on these two kinds of Distributions are formulated by quadratic programming problems. It can be said that a portfolio return based on the lower Possibility Distribution has smaller Possibility spread than the one on the upper Possibility Distribution. In addition, a Possibility risk can be defined as an interval given by the spreads of the portfolio returns from the upper and the lower Possibility Distributions to reflect the uncertainty in real investment problems. A numerical example of a portfolio selection problem is given to illustrate our proposed approaches.
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Theory and Methodology Portfolio selection based on upper and lower exponential Possibility Distributions
1999Co-Authors: Hideo Tanaka, Peijun GuoAbstract:In this paper, two kinds of Possibility Distributions, namely, upper and lower Possibility Distributions are identified to reflect experts’ knowledge in portfolio selection problems. Portfolio selection models based on these two kinds of Distributions are formulated by quadratic programming problems. It can be said that a portfolio return based on the lower Possibility Distribution has smaller Possibility spread than the one on the upper Possibility Distribution. In addition, a Possibility risk can be defined as an interval given by the spreads of the portfolio returns from the upper and the lower Possibility Distributions to reflect the uncertainty in real investment problems. A numerical example of a portfolio selection problem is given to illustrate our proposed approaches. ” 1999 Elsevier Science B.V. All rights reserved.
Ronald R. Yager - One of the best experts on this subject based on the ideXlab platform.
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On the instantiation of Possibility Distributions
Fuzzy Sets and Systems, 2002Co-Authors: Ronald R. YagerAbstract:We investigate the problem of instantiating a variable whose value is uncertain, but known to be constrained by a Possibility Distribution. Using a model based upon the Dempster-Shafer belief structure, we show that this problem of instantiation is analogous to a compound experiment in which we randomly select a subset and then perform a number of repeated experiments without replacement on this set. The probability Distribution resulting from this compound experiment leads to a random procedure for instantiating a Possibility Distribution.
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On the specificity of a Possibility Distribution
Fuzzy Sets and Systems, 1992Co-Authors: Ronald R. YagerAbstract:Abstract The specificity of a Possibility Distribution measures the degree to which the Distribution allows one and only one element as its manifestation. As such it is a measure of amount of uncertainty or information. We investigate a number of issues related to specificity measures. We discuss the connection between the specificity of a Possibility Distribution and the entropy of a probability Distribution. We describe unifying view for constructing specificity measures. We look at the relationship of the specificity of a Distribution and its negation. We consider the case where the base set is continuous.
Robert Fullér - One of the best experts on this subject based on the ideXlab platform.
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Interactions Between Computational Intelligence and Mathematics (2) - On the lower limit for possibilistic correlation coefficient with identical marginal Possibility Distributions
Studies in Computational Intelligence, 2018Co-Authors: István Á. Harmati, Robert FullérAbstract:In 2011 Fuller et al. [An improved index of interactivity for fuzzy numbers, Fuzzy Sets and Systems, 165 (2011), pp. 50–60] introduced a new measure of interactivity between fuzzy numbers (interpreted as Possibility Distributions), called the weighted possibilistic correlation coefficient, which can be determined from their joint Possibility Distribution. They also left two questions open regarding the lower limit of the weighted possibilistic correlation coefficient of marginal Possibility Distribution with the same membership function. In this paper we will answer these questions not only in the case of fuzzy numbers, but also for quasi fuzzy numbers.
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Nguyen type theorem for extension principle based on a joint Possibility Distribution
International Journal of Approximate Reasoning, 2018Co-Authors: Lucian Coroianu, Robert FullérAbstract:Abstract In this paper, first we prove that making abstraction of the output obtained from the interactive extension principle based on a joint Possibility Distribution, in the case of unimodal fuzzy numbers and when the function that generates the operation is continuous and strictly increasing in each argument restricted to the support of each fuzzy number used in the process, then we can use joint Possibility Distributions with the property that the left/right side of the output is obtained from the convolution of the values in the left/right side of these fuzzy numbers. Then, considering joint Possibility Distributions with the aforementioned property, we find an Nguyen type characterization of the level sets of the output based on interactive extension principle, in terms of the level sets of the fuzzy numbers used in the process. These two key results complete well-known results obtained in the case of Zadeh's extension principle and also in the case of triangular norm-based extension principle. As an interesting corollary, in the special case of unimodal fuzzy numbers, the Nguyen theorem can be used to present a new proof concerning necessary and sufficient conditions on the equality of the outputs based on joint Possibility Distributions, respectively based on Zadeh's extension principle.
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Probabilistic versus possibilistic risk assessment models for optimal service level agreements in grid computing
Information Systems and e-Business Management, 2013Co-Authors: Christer Carlsson, Robert FullérAbstract:We present a probabilistic and a possibilistic model for assessing the risk of a service level agreement for a computing task in a cluster/grid environment. These models can also be applied to cloud computing. Using the predictive probabilistic approach we develop a framework for resource management in grid computing, and by introducing an upper limit for the number of failures we approximate the probability that a particular computing task is successful. In the predictive Possibility model we estimate the Possibility Distribution of the future number of node failures by a fuzzy nonparametric regression technique. Then the resource provider can use the probabilistic or the possibilistic model to get alternative risk assessments.
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Probabilistic correlation coefficients for Possibility Distributions
2011 15th IEEE International Conference on Intelligent Engineering Systems, 2011Co-Authors: Robert Fullér, István Á. Harmati, Péter VárlakiAbstract:The goal of this paper to introduce two alternative definitions for the possibilistic correlation coefficient by equipping the level sets of a joint Possibility Distribution with nonuniform probability Distributions which are directly derived from the shape function of the joint Possibility Distribution. We also show some examples for their exact calculation for joint Possibility Distributions defined by Mamdani, Łukasiewicz and Larsen triangular norms.
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A Normative View on Possibility Distributions
Possibility for Decision, 2011Co-Authors: Christer Carlsson, Robert FullérAbstract:In probability theory the expected value of functions of random variables plays a fundamental role in defining the basic characteristic measures of probability Distributions. For example, the variance, covariance and correlation of random variables can be computed as the expected value of their appropriately chosen real-valued functions. In Possibility theory we can use the principle of expected value of functions on fuzzy sets to define variance, covariance and correlation of Possibility Distributions. Marginal probability Distributions are determined from the joint one by the principle of ‘falling integrals’ and marginal Possibility Distributions are determined from the joint Possibility Distribution by the principle of ‘falling shadows’. Probability Distributions can be interpreted as carriers of incomplete information [203], and Possibility Distributions can be interpreted as carriers of imprecise information.
