How To Take Into Account Dependence Between the Inputs: From Interval Computations to Constraint-Rel

In many real-life situations, in addition to knowing the intervals xi of possible values of each variable xi, we also know additional restrictions on the possible combinations of xi; in this case, the set x of possible values of x = (x1;:::;xn) is a proper subset of the original box x1£:::£xn. In this paper, we show how to take into account this dependence between the inputs when computing the range of a function f(x1;:::;xn). c

[1]  Harrison M. Wadsworth Handbook of Statistical Methods for Engineers and Scientists , 1990 .

[2]  R. Nelsen An Introduction to Copulas , 1998 .

[3]  S. Vavasis Nonlinear optimization: complexity issues , 1991 .

[4]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[5]  Andrzej Skowron,et al.  Rough Sets , 1995, Lecture Notes in Computer Science.

[6]  Grzegorz Kondrak,et al.  Biomedical Term Recognition with the Perceptron HMM Algorithm , 2006, BioNLP@NAACL-HLT.

[7]  Jennifer Widom,et al.  A first course in database systems (2. ed.) , 2002 .

[8]  Grzegorz Kondrak,et al.  Applying Many-to-Many Alignments and Hidden Markov Models to Letter-to-Phoneme Conversion , 2007, NAACL.

[9]  V. Kreinovich Computational Complexity and Feasibility of Data Processing and Interval Computations , 1997 .

[10]  R. Baierlein Probability Theory: The Logic of Science , 2004 .

[11]  John A. Hole,et al.  Nonlinear high‐resolution three‐dimensional seismic travel time tomography , 1992 .

[12]  Berthold Schweizer Introduction to Copulas , 2007 .

[13]  Vladik Kreinovich,et al.  Taylor Model-Type Techniques for Handling Uncertainty in Expert Systems , 2005 .

[14]  Vladik Kreinovich,et al.  Interval-type and affine arithmetic-type techniques for handling uncertainty in expert systems , 2007, Journal of Computational and Applied Mathematics.

[15]  Colin A. Zelt,et al.  Three‐dimensional seismic refraction tomography: A comparison of two methods applied to data from the Faeroe Basin , 1998 .

[16]  Vladik Kreinovich,et al.  Using expert knowledge in solving the seismic inverse problem , 2005, NAFIPS 2005 - 2005 Annual Meeting of the North American Fuzzy Information Processing Society.

[17]  R. Parker Geophysical Inverse Theory , 1994 .

[18]  Luc Jaulin,et al.  Applied Interval Analysis , 2001, Springer London.

[19]  Sittichai Jiampojamarn,et al.  Two Experiments in Biological Term Annotation using Classification Methods , 2004 .

[20]  Colin Cherry,et al.  Biomedical Term Recognition Using Discriminative Training , 2022 .

[21]  Eldon R. Hansen,et al.  Sharpness in Interval Computations , 1997, Reliab. Comput..

[22]  Jennifer Widom,et al.  A First Course in Database Systems , 1997 .

[23]  Alex M. Andrew,et al.  Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics , 2002 .

[24]  N. Cercone,et al.  Secure Mail Transfer Protocol ( SecMTP ) , 2003 .

[25]  Vladik Kreinovich,et al.  Exact Bounds on Finite Populations of Interval Data , 2005, Reliab. Comput..

[26]  Nick Cercone,et al.  Biological Named Entity Recognition Using n-grams and Classification Methods , 2005 .

[27]  Vladik Kreinovich,et al.  Ellipsoids and ellipsoid-shaped fuzzy sets as natural multi-variate generalization of intervals and fuzzy numbers: How to elicit them from users, and how to use them in data processing , 2007, Inf. Sci..

[28]  Sanjeev Chopra,et al.  Affine arithmetic-type techniques for handling uncertainty in expert systems , 2005 .