Improving Accuracy in Importance Sampling: An Integrated Approach with Fuzzy-Strata Sampling

Document Type : Original Article

Authors

1 Aerospace Research Institute

2 Lecturer and Researcher in Computer Science

Abstract

Several statistical approaches have been developed to analyze the sampling of huge data and information. There are three significant factors for comparison of the strength of these methods that are argued in this paper; the proposed method is a compatible approach to various types of sampling methods and applied to improve the sampling efficiency and decrease uncertainties to reach accuracy in results. In argued methods, each element just belongs to one category and/ or strata, but in our approach, each element includes all groups with one exception that membership values are different. The case study results show that the proposed Fuzzy Strata Sampling (FSS) method better measures uncertainty and accuracy rate than the other existing sampling methods.

Keywords

Main Subjects


[1]   M. Nadjafi, M.A. Farsi, and A. Najafi, Uncertainty improving in importance sampling: An integrated approach with Fuzzy-Cluster sampling, 24th annual European Safety and Reliability (ESREL) Conference, Wroclaw, Poland, 14-18 September, 2014.
[2].  Kurowicka, D. and R.M. Cooke, Uncertainty analysis with high dimensional dependence modelling. 2006: John Wiley & Sons.
[3].  Ondrej Linda and M. Manic, 'Importance Sampling Based Defuzzification for General Type-2 Fuzzy Sets',WCCI 2010 IEEE World Congress on Computational Intelligence, July, 18-23, 2010 - CCIB, Barcelona, Spain.
[4].  Verdonck, F.A., et al., Improving uncertainty analysis in European Union risk assessment of chemicals. Integrated environmental assessment and management, 2007. 3(3): p. 333-343.
[5].  Kwakernaak, H., Fuzzy random variables—I. Definitions and theorems. Information Sciences, 1978. 15(1): p. 1-29.
[6].  L. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets Syst. 1 (1978) 3-28.
[7].  Viertl, R., Statistical methods for fuzzy data. 2011: Wiley. com.
[8].  Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning—I. Information sciences, 1975. 8(3): p. 199-249.
[9].  Garibaldi, J.M. and R.I. John. Choosing membership functions of linguistic terms. in Fuzzy Systems, 2003. FUZZ'03. The 12th IEEE International Conference on. 2003. IEEE.
[10]. Bethlehem, J., The rise of survey sampling. CBS Discussion Paper, 2009. 9015.
[11]. Institute, S., SAS/STAT 12. 1 User's Guide: Survey Data Analysis (Book Excerpt). 2012: SAS Institute.
[12]. Levy, P.S. and S. Lemeshow, Sampling of populations: methods and applications. 2013: John Wiley & Sons.
[13]. Hansen, M.H. and W.N. Hurwitz, Sample survey methods and theory. Vol. I. 1953.
[14]. Grøn, C., et al., Uncertainty from sampling–A Nordtest handbook for sampling planners on sampling quality assurance and uncertainty estimation. Nordtest Report TR, 2007. 604.
[15]. Billinton, R. and R.N. Allan, Reliability evaluation of engineering systems: concepts and techniques. 1983: Plenum Press New York, NY.
[16]. Molenberghs, G., Survey methods and sampling techniques. Limburg, Belgium: Center for Statistics, Universiteit Hasselt, 2008.
[17]. Lyberg, L.E., et al., Survey measurement and process quality. Vol. 999. 2012: John Wiley & Sons.
[18]. Lohr, S., Sampling: design and analysis. 2009: Cengage Learning.
[19]. Chaudhuri, A. and H. Stenger, Survey sampling: theory and methods. 2010: CRC Press.
[20]. Cochran, W.G., Sampling techniques. 2007: John Wiley & Sons.
[21]. Ghufran, Shazia, Srikant Gupta, and Aquil Ahmed. "A fuzzy compromise approach for solving multi-objective stratified sampling design." Neural Computing and Applications 33.17 (2021): 10829-10840.
[22]. Mradula, et al. "Efficient estimation of population mean under stratified random sampling with linear cost function." Communications in Statistics-Simulation and Computation (2019): 1-24.
[23]. Haq, Ahteshamul, Irfan Ali, and Rahul Varshney. "Compromise allocation problem in multivariate stratified sampling with flexible fuzzy goals." Journal of Statistical Computation and Simulation 90.9 (2020): 1557-1569.
[24]. Taverniers, Søren, and Daniel M. Tartakovsky. "Estimation of distributions via multilevel Monte Carlo with stratified sampling." Journal of Computational Physics 419 (2020): 109572.
 
 
 
Volume 4, Issue 1
January 2021
Pages 61-67
  • Receive Date: 02 August 2021
  • Revise Date: 07 October 2021
  • Accept Date: 11 October 2021
  • First Publish Date: 11 October 2021