Author

# Marie-Hélène Masson

Other affiliations: Centre national de la recherche scientifique

Bio: Marie-Hélène Masson is an academic researcher from University of Technology of Compiègne. The author has contributed to research in topics: Fuzzy number & Fuzzy logic. The author has an hindex of 7, co-authored 10 publications receiving 394 citations. Previous affiliations of Marie-Hélène Masson include Centre national de la recherche scientifique.

##### Papers

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TL;DR: This paper proposes to characterize the probabilities of the different classes by simultaneous confidence intervals with a given confidence level [email protected] from this imprecise specification, a procedure for constructing a possibility distribution is described, insuring that the resulting possibility distribution will dominate the true probability distribution in at least 100% of the cases.

111 citations

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TL;DR: Nonparametric rank-based statistics depending only on linear orderings of the observations are extended to fuzzy data, leading to the concepts of fuzzy p-value, and graded rejection of the null hypothesis at a given significance level.

93 citations

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TL;DR: This method is extended to the case where dissimilarities are only known to lie within certain intervals, and shows the ability of this method to represent both the structure and the precision of dissimilarity measurements.

67 citations

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TL;DR: This paper describes an extension of principal component analysis allowing the extraction of a limited number of relevant features from high-dimensional fuzzy data, and the concept of correlation coefficient is extended to fuzzy numbers, allowing the interpretation of the new features in terms of the original variables.

Abstract: This paper describes an extension of principal component analysis (PCA) allowing the extraction of a limited number of relevant features from high-dimensional fuzzy data. Our approach exploits the ability of linear autoassociative neural networks to perform information compression in just the same way as PCA, without explicit matrix diagonalization. Fuzzy input values are propagated through the network using fuzzy arithmetics, and the weights are adjusted to minimize a suitable error criterion, the inputs being taken as target outputs. The concept of correlation coefficient is extended to fuzzy numbers, allowing the interpretation of the new features in terms of the original variables. Experiments with artificial and real sensory evaluation data demonstrate the ability of our method to provide concise representations of complex fuzzy data.

56 citations

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TL;DR: This paper extendsMultidimensional scaling to the case where dissimilarities are expressed as intervals or fuzzy numbers, and each object is no longer represented by a point but by a crisp or a fuzzy region.

30 citations

##### Cited by

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TL;DR: An overview of numerical possibility theory is proposed, showing that some notions in statistics are naturally interpreted in the language of this theory and providing a natural definition of a subjective possibility distribution that sticks to the Bayesian framework of exchangeable bets.

411 citations

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TL;DR: This work proposes a variant of the EM algorithm that iteratively maximizes the maximization of a generalized likelihood criterion, which can be interpreted as a degree of agreement between the statistical model and the uncertain observations.

Abstract: We consider the problem of parameter estimation in statistical models in the case where data are uncertain and represented as belief functions. The proposed method is based on the maximization of a generalized likelihood criterion, which can be interpreted as a degree of agreement between the statistical model and the uncertain observations. We propose a variant of the EM algorithm that iteratively maximizes this criterion. As an illustration, the method is applied to uncertain data clustering using finite mixture models, in the cases of categorical and continuous attributes.

249 citations

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01 Jan 2003TL;DR: Probability theory has had an almost unquestioned foundation since Kolmogorov (1933) as mentioned in this paper, and it may be expressed as total preorders on a system of subsets of events.

Abstract: Probability theory has had an almost unquestioned foundation since Kolmogorov (1933) [111]. Probability is a (normalized) measure on an algebra of events i.e. subsets of an arbitrary set. The probability of an event may be a result in a theory about any part of the real world. It may be an assumption that the beliefs or knowledge of agents can be expressed as total preorders on a system of subsets of events. Theorem 9 page 98 then gives probability as a representation of this relation. Under the assumptions of this representation theorem the two assumptions — a total preorder on an algebra or a probability measure on this algebra — are therefore equivalent.

238 citations

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TL;DR: The main fuzzy approaches for defining spatial relationships including topological (set relationships, adjacency) and metrical relations (distances, directional relative position) are reviewed.

232 citations

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TL;DR: In spite of a growing literature concerning the development and application of fuzzy techniques in statistical analysis, the need is felt for a more systematic insight into the potentialities of cross fertilization between Statistics and Fuzzy Logic.

129 citations