{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,21]],"date-time":"2024-02-21T23:40:50Z","timestamp":1708558850266},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2007,12,1]],"date-time":"2007-12-01T00:00:00Z","timestamp":1196467200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Reliable Comput"],"published-print":{"date-parts":[[2007,12]]},"DOI":"10.1007\/s11155-007-9045-6","type":"journal-article","created":{"date-parts":[[2008,2,4]],"date-time":"2008-02-04T19:22:00Z","timestamp":1202152920000},"page":"467-488","source":"Crossref","is-referenced-by-count":11,"title":["Computing Population Variance and Entropy under Interval Uncertainty: Linear-Time Algorithms"],"prefix":"10.1007","volume":"13","author":[{"given":"Gang","family":"Xiang","sequence":"first","affiliation":[]},{"given":"Martine","family":"Ceberio","sequence":"additional","affiliation":[]},{"given":"Vladik","family":"Kreinovich","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,2,5]]},"reference":[{"key":"9045_CR1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-4090-5","volume-title":"Lectures in Functional Analysis and Operator Theory","author":"S. Berberian","year":"1974","unstructured":"Berberian S. (1974) Lectures in Functional Analysis and Operator Theory. Springer, New York, Heidelberg, Berlin"},{"key":"9045_CR2","doi-asserted-by":"crossref","unstructured":"Boyd, S. and Vandenberghe, L.: Convex Optimization, Cambridge University Press, 2004.","DOI":"10.1017\/CBO9780511804441"},{"key":"9045_CR3","doi-asserted-by":"crossref","unstructured":"van der Broek, P. and Noppen, J.: Fuzzy Weighted Average: Alternative Approach, in: Proceedings of the 25th International Conference of the North American Fuzzy Information Processing Society NAFIPS\u20192006, Montreal, Quebec, Canada, June 3\u20136, 2006.","DOI":"10.1109\/NAFIPS.2006.365872"},{"key":"9045_CR4","volume-title":"Introduction to Algorithms","author":"Th.H. Cormen","year":"2001","unstructured":"Cormen Th.H., Leiserson C.E., Rivest R.L., Stein C. (2001) Introduction to Algorithms. MIT Press, Cambridge"},{"issue":"4","key":"9045_CR5","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s11155-006-9001-x","volume":"12","author":"E. Dantsin","year":"2006","unstructured":"Dantsin E., Kreinovich V., Wolpert A., Xiang G. (2006) Population Variance under Interval Uncertainty: A New Algorithm. Reliable Computing 12(4):273\u2013280","journal-title":"Reliable Computing"},{"key":"9045_CR6","unstructured":"Dantsin, E., Wolpert, A., Ceberio, M., Xiang, G., and Kreinovich, V.: Detecting Outliers under Interval Uncertainty: A New Algorithm Based on Constraint Satisfaction, in: Proceedings of the International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems IPMU\u201906, Paris, France, July 2\u20137, 2006, pp. 802\u2013809."},{"issue":"3","key":"9045_CR7","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s11155-005-3616-1","volume":"11","author":"S. Ferson","year":"2005","unstructured":"Ferson S., Ginzburg L., Kreinovich V., Longpr\u00e9 L., Aviles M. (2005) Exact Bounds on Finite Populations of Interval Data. Reliable Computing 11(3):207\u2013233","journal-title":"Reliable Computing"},{"key":"9045_CR8","doi-asserted-by":"crossref","unstructured":"Ferson, S., Kreinovich, V., Hajagos, J., Oberkampf, W., and Ginzburg, L.: Experimental Uncertainty Estimation and Statistics for Data Having Interval Uncertainty, Sandia National Laboratories, Report SAND2007-0939, 2007.","DOI":"10.2172\/910198"},{"key":"9045_CR9","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1007\/BF01582890","volume":"52","author":"P. Hansen","year":"1991","unstructured":"Hansen P., de Aragao M.V.P., Ribeiro C.C. (1991) Hyperbolic 0-1 Programming and Optimization in Information Retrieval. Math. Programming 52:255\u2013263","journal-title":"Math. Programming"},{"key":"9045_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4471-0249-6","volume-title":"Applied Interval Analysis: with Examples in Parameter and State Estimation, Robust Control and Robotics","author":"L. Jaulin","year":"2001","unstructured":"Jaulin L., Kieffer M., Didrit O., Walter E. (2001) Applied Interval Analysis: with Examples in Parameter and State Estimation, Robust Control and Robotics. Springer Verlag, London"},{"key":"9045_CR11","doi-asserted-by":"crossref","DOI":"10.1002\/0471755575","volume-title":"Uncertainty and Information: Foundations of Generalized Information Theory","author":"G.J. Klir","year":"2005","unstructured":"Klir G.J. (2005) Uncertainty and Information: Foundations of Generalized Information Theory. J. Wiley, Hoboken, New Jersey"},{"issue":"1","key":"9045_CR12","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/BF02388188","volume":"2","author":"V. Kreinovich","year":"1996","unstructured":"Kreinovich V. (1996) Maximum Entropy and Interval Computations. Reliable Computing 2(1):63\u201379","journal-title":"Reliable Computing"},{"issue":"1","key":"9045_CR13","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/s11155-005-5943-7","volume":"11","author":"V. Kreinovich","year":"2005","unstructured":"Kreinovich V., Longpr\u00e9 L., Patangay P., Ferson S., Ginzburg L. (2005) Outlier Detection under Interval Uncertainty: Algorithmic Solvability and Computational Complexity. Reliable Computing 11(1):59\u201376","journal-title":"Reliable Computing"},{"issue":"6","key":"9045_CR14","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1007\/s11155-006-9015-4","volume":"12","author":"V. Kreinovich","year":"2006","unstructured":"Kreinovich V., Xiang G., Starks S.A., Longpr\u00e9 L., Ceberio M., Araiza R., Beck J., Kandathi R., Nayak A., Torres R., Hajagos J. (2006) Towards Combining Probabilistic and Interval Uncertainty in Engineering Calculations: Algorithms for Computing Statistics under Interval Uncertainty, and Their Computational Complexity. Reliable Computing 12(6):471\u2013501","journal-title":"Reliable Computing"},{"key":"9045_CR15","doi-asserted-by":"crossref","unstructured":"Nivlet, P., Fournier, F., and Royer, J.: A New Methodology to Account for Uncertainties in 4-D Seismic Interpretation, in: Proc. 71st Annual Int\u2019l Meeting of Soc. of Exploratory Geophysics SEG\u20192001, San Antonio, September 9\u201314, 2001, pp. 1644\u20131647.","DOI":"10.1190\/1.1816431"},{"key":"9045_CR16","doi-asserted-by":"crossref","unstructured":"Nivlet, P., Fournier, F., and Royer, J.: Propagating Interval Uncertainties in Supervised Pattern Recognition for Reservoir Characterization, in: Proc. 2001 Society of Petroleum Engineers Annual Conf. SPE\u20192001, New Orleans, September 30\u2013October 3, 2001, paper SPE-71327.","DOI":"10.2118\/71327-MS"},{"key":"9045_CR17","unstructured":"Rabinovich, S.: Measurement Errors: Theory and Practice, American Institute of Physics, New York, 1993."},{"key":"9045_CR18","volume-title":"Convex Functions","author":"A.W. Roberts","year":"1973","unstructured":"Roberts A.W., Varberg D.E. (1973) Convex Functions. Academic Press, New York and London"},{"key":"9045_CR19","volume-title":"Nonlinear Optimization: Complexity Issues","author":"S.A. Vavasis","year":"1991","unstructured":"Vavasis S.A. (1991) Nonlinear Optimization: Complexity Issues. Oxford Science, New York"},{"key":"9045_CR20","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198531470.001.0001","volume-title":"Convexity","author":"R. Webster","year":"1994","unstructured":"Webster R. (1994) Convexity. Oxford University Press, Oxford, New York, Tokyo"},{"key":"9045_CR21","unstructured":"Xiang, G., Kosheleva, O., and Klir, G. J.: Estimating Information Amount under Interval Uncertainty: Algorithmic Solvability and Computational Complexity, in: Proceedings of the International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems IPMU\u201906, Paris, France, July 2\u20137, 2006, pp. 840\u2013847."}],"container-title":["Reliable Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11155-007-9045-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11155-007-9045-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11155-007-9045-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,21]],"date-time":"2024-02-21T22:50:26Z","timestamp":1708555826000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11155-007-9045-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,12]]},"references-count":21,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2007,12]]}},"alternative-id":["9045"],"URL":"https:\/\/doi.org\/10.1007\/s11155-007-9045-6","relation":{},"ISSN":["1385-3139","1573-1340"],"issn-type":[{"value":"1385-3139","type":"print"},{"value":"1573-1340","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,12]]}}}