A new distance for fuzzy descriptions of measurements

http://www.imeko.org/publications/wc-2006/PWC-2006-TC7-018u.pdfInternational audienceFuzzy nominal scales were introduced in order to propose a formalism to the representation of empirical quantities by fuzzy subsets of words. This paper presents the results of studies on distances associated to this formalism and proposes a new distance operator

The transportation distance for fuzzy descriptions of measurement

International audienceFuzzy nominal scales were introduced in order to propose a formalism to the representation of empirical quantities by fuzzy subsets of words. This scale proposes a similarity relation and an associated bounded distance that can be used to perform signal processing on fuzzy subsets of words. Due to the limits of this last distance, we studied distances associated to this formalism and proposed a new distance operator named transportation distance. This paper presents the results of these studies

Fuzzy knowledge-based recognition of internal structures of the head

Nous proposons une méthode basée sur la connaissance a priori pour la segmentation et la reconnaissance des formes des structures internes du cerveau en IRM. Les connaissances sur les formes des structures et les distances entre elles, provenant de l'atlas de Talairach, sont modélisées par un champ flou en utilisant une analogie avec la distribution du potentiel d'électrostatique. Une sur-segmentation est d'abord effectuée sur le cerveau pour obtenir des régions homogènes. La reconnaissance des structures est ensuite obtenue par la classification des régions utilisant un algorithme génétique, suivie par un affinement au niveau du pixel. Les connaissances floues modélisées sont utilisées dans ces deux étapes. La performance de la méthode proposée est validée par référence aux résultats manuels en utilisant 4 indices de quantification

Characterization of approximate plane symmetries for 3D fuzzy objects

International audienceWe are interested in finding and characterizing the symmetry planes of fuzzy objects in 3D space. We introduce first a fuzzy symmetry measure which defines an object symmetry degree with respect to a given plane. It is computed by measuring the similarity between the original object and its reflection. The choice of an appropriate measure of comparison is based on the desired properties. In a second part, a method for finding the best symmetry planes of fuzzy objects is proposed. We then apply these results to the representation of directional relationships

K-nearest neighbor search for fuzzy objects

The K-Nearest Neighbor search (kNN) problem has been investigated extensively in the past due to its broad range of applications. In this paper we study this problem in the context of fuzzy objects that have indeterministic boundaries. Fuzzy objects play an important role in many areas, such as biomedical image databases and GIS. Existing research on fuzzy objects mainly focuses on modelling basic fuzzy object types and operations, leaving the processing of more advanced queries such as kNN query untouched. In this paper, we propose two new kinds of kNN queries for fuzzy objects, Ad-hoc kNN query (AKNN) and Range kNN query (RKNN), to find the k nearest objects qualifying at a probability threshold or within a probability range. For efficient AKNN query processing, we optimize the basic best-first search algorithm by deriving more accurate approximations for the distance function between fuzzy objects and the query object. To improve the performance of RKNN search, effective pruning rules are developed to significantly reduce the search space and further speed up the candidate refinement process. The efficiency of our proposed algorithms as well as the optimization techniques are verified with an extensive set of experiments using both synthetic and real datasets

Distances in evidence theory: Comprehensive survey and generalizations

AbstractThe purpose of the present work is to survey the dissimilarity measures defined so far in the mathematical framework of evidence theory, and to propose a classification of these measures based on their formal properties. This research is motivated by the fact that while dissimilarity measures have been widely studied and surveyed in the fields of probability theory and fuzzy set theory, no comprehensive survey is yet available for evidence theory. The main results presented herein include a synthesis of the properties of the measures defined so far in the scientific literature; the generalizations proposed naturally lead to additions to the body of the previously known measures, leading to the definition of numerous new measures. Building on this analysis, we have highlighted the fact that Dempster’s conflict cannot be considered as a genuine dissimilarity measure between two belief functions and have proposed an alternative based on a cosine function. Other original results include the justification of the use of two-dimensional indexes as (cosine; distance) couples and a general formulation for this class of new indexes. We base our exposition on a geometrical interpretation of evidence theory and show that most of the dissimilarity measures so far published are based on inner products, in some cases degenerated. Experimental results based on Monte Carlo simulations illustrate interesting relationships between existing measures