Research ArticleOpen AccessGoogle Scholar indexed
Monotonic Vector Space Model (Ⅰ): Concepts and Operations
National University of Defense Technology, Changsha, China
- 1 National University of Defense Technology, Changsha, China
American Journal of Operations Research·Volume 04 (2014)·Pages 30–41·Published 6 January 2014·DOI10.4236/ajor.2014.41004
Copy link · social · email
Abstract
Monotonic vector space (MVS), as a novel model in which there exist some monotonic mappings, is proposed. MVS model is an abstract of many practical problems (such as image processing, system capability engineering, etc.) and includes many useful important operations. This paper, as the first one of series papers, discusses the MVS framework, relative important concepts and important operations including partition, synthesis, screening, sampling, etc. And algorithms for these operations are the focus of this paper. The application of these opera tions in system capability engineering will be dealt with in the second part of this series of papers.
KeywordsMonotonic Vector SpaceOperationsPartitionSynthesisScreeningSampling
- J. W. Hu, et al., “MIS Method (Monotonic Indices Space) and Its Application in Capability Indicators Effectiveness Analysis of a Notional Anti-Stealth Information System,” IEEE Transactions on Systems, Man and Cybernetics PART A, Vol. 39, No. 2, 2009, pp. 407-417.
- V. Bouthonnier and A. H. Levis, “System Effectiveness Analysis of C3 Systems,” IEEE Transactions on Systems, Man and Cybernetics, Vol. SMC-14, No.1, 1984, pp. 48-54. http://dx.doi.org/10.1109/TSMC.1984.6313268
- M. D. McKay, et al., “A Comparision of Three Methods for Selecting Values of Input Variablea in Analysis of Output from a Computer Codes,” Tehchnometrics, Vol. 21, No. 2, 1979, pp. 239-245.
- B. Bettonvil, “Detection of Important Factors by Sequential Bifurcation,” Ph.D. Dissertation, Tilburg University Press, Tilburg, 1996.
- B. Bettonvil and J. P. C. Kleijnen, “Searching for Important Factors in Simulation Models with Many Factors: Sequential Bifurcation,” European Journal of Operational Research, Vol. 96, No. 1, 1997, pp. 180-194. http://dx.doi.org/10.1016/S0377-2217(96)00156-7
- J. P. C. Kleijnen, B. Bettonvil and F. Persson, “Screening for the Important Factors in Large Discrete-Event Simulation: Sequential Bifurcation and Its Applications,” In: A. Dean and S. Lewis, Eds., Screening: Methods for Experimentation in Industry, Drug Discovery, and Genetics, Springer-Verlag, New York, 2006, pp. 287-307. http://dx.doi.org/10.1007/0-387-28014-6_13
- H. Wan, B. E. Ankenman and B. L. Nelson, “Controlled Sequential Bifurcation: A New Factor-Screening Method for DiscreteEvent Simulation,” Operations Research, Vol. 54, No. 4, 2006, pp. 743-755. http://dx.doi.org/10.1287/opre.1060.0311
- R. C. H. Cheng, “Searching for Important Factors: Sequential Bifurcation under Uncertainty,” Proceedings of the 1997 Winter Simulation Conference, 1997, pp. 275-280.
- B. E. Ankenman, R. C. H. Cheng and S. M. Lewis, “A Polytope Method for Estimating Factor Main Effects Efficiently,” Proceedings of the 2006 Winter Simulation Conference, Monterey, 3-6 December 2006. http://dx.doi.org/10.1109/WSC.2006.323104
- R. Agrawal and R. Srikant, “Fast Algorithms for Mining Association Rules,” Proceedings of 1994 International Conference Very Large Data Bases (VLDB’94), Santiago, September 1994.
- B. Chazelle and L. Palios, “Triangulating a Non-Convex Polytope,” Discrete & Computational Geometry, Vol. 5, No. 1, 1990, pp. 505-526. http://dx.doi.org/10.1007/BF02187807