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Random Fuzzy Sets and Their Applications
"... This chapter presents a rigorous theory of random fuzzy sets in its most general form. Some applications are included. ..."
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This chapter presents a rigorous theory of random fuzzy sets in its most general form. Some applications are included.
Integrals of Random Fuzzy Sets
"... This paper tries to give a systematic investigation of integration of random fuzzy sets. Besides the widely used Aumannintegral adaptions of Pettis and Bochnerintegration for random elements in Banach spaces are introduced. The mutual relationships of these competing concepts will be explored comp ..."
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Cited by 2 (0 self)
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This paper tries to give a systematic investigation of integration of random fuzzy sets. Besides the widely used Aumannintegral adaptions of Pettis and Bochnerintegration for random elements in Banach spaces are introduced. The mutual relationships of these competing concepts will be explored
RANDOM FUZZY SETS
"... It is well known that in decision making under uncertainty, while we are guided by a general (and abstract) theory of probability and of statistical inference, each specific type of observed data requires its own analysis. Thus, while textbook techniques treat precisely observed data in multivariate ..."
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Cited by 2 (1 self)
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elements, i.e., we need to place random fuzzy data completely within the rigorous theory of probability. This chapter presents the most general framework for random fuzzy data, namely the framework of random fuzzy sets. We also describe several applications of this framework.
Extreme probability distributions of random/fuzzy sets and pboxes
"... Abstract: Uncertain information about a system variable described by a random set or an equivalent DempsterShafer structure on a finite space of singletons determines an infinite convex set of probability distributions, given by the convex hull of a finite set of extreme distributions. Extreme dist ..."
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applications to random sets with nested focal elements (consonant random sets or the equivalent fuzzy set) and to pboxes. A simple direct procedure to derive extreme distributions from a pbox is described through simple numerical examples.
RANDOM FUZZY SETS: A MATHEMATICAL TOOL TO DEVELOP STATISTICAL FUZZY DATA ANALYSIS
"... Abstract. Data obtained in association with many reallife random experiments from different fields cannot be perfectly/exactly quantified. Often the underlying imprecision can be suitably described in terms of fuzzy numbers/ values. For these random experiments, the scale of fuzzy numbers/values e ..."
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/values enables to capture more variability and subjectivity than that of categorical data, and more accuracy and expressiveness than that of numerical/vectorial data. On the other hand, random fuzzy numbers/sets model the random mechanisms generating experimental fuzzy data, and they are soundly formalized
Randomized Algorithms
, 1995
"... Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available, or the simp ..."
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Cited by 2210 (37 self)
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Randomized algorithms, once viewed as a tool in computational number theory, have by now found widespread application. Growth has been fueled by the two major benefits of randomization: simplicity and speed. For many applications a randomized algorithm is the fastest algorithm available
Inducing Features of Random Fields
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1997
"... We present a technique for constructing random fields from a set of training samples. The learning paradigm builds increasingly complex fields by allowing potential functions, or features, that are supported by increasingly large subgraphs. Each feature has a weight that is trained by minimizing the ..."
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Cited by 664 (14 self)
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We present a technique for constructing random fields from a set of training samples. The learning paradigm builds increasingly complex fields by allowing potential functions, or features, that are supported by increasingly large subgraphs. Each feature has a weight that is trained by minimizing
CURE: An Efficient Clustering Algorithm for Large Data sets
 Published in the Proceedings of the ACM SIGMOD Conference
, 1998
"... Clustering, in data mining, is useful for discovering groups and identifying interesting distributions in the underlying data. Traditional clustering algorithms either favor clusters with spherical shapes and similar sizes, or are very fragile in the presence of outliers. We propose a new clustering ..."
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Cited by 713 (5 self)
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of random sampling and partitioning. A random sample drawn from the data set is first partitioned and each partition is partially clustered. The partial clusters are then clustered in a second pass to yield the desired clusters. Our experimental results confirm that the quality of clusters produced by CURE
Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. Technical Report 2003/235, Cryptology ePrint archive, http://eprint.iacr.org, 2006. Previous version appeared at EUROCRYPT 2004
 34 [DRS07] [DS05] [EHMS00] [FJ01] Yevgeniy Dodis, Leonid Reyzin, and Adam
, 2004
"... We provide formal definitions and efficient secure techniques for • turning noisy information into keys usable for any cryptographic application, and, in particular, • reliably and securely authenticating biometric data. Our techniques apply not just to biometric information, but to any keying mater ..."
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Cited by 532 (38 self)
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material that, unlike traditional cryptographic keys, is (1) not reproducible precisely and (2) not distributed uniformly. We propose two primitives: a fuzzy extractor reliably extracts nearly uniform randomness R from its input; the extraction is errortolerant in the sense that R will be the same even
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