Optimizing Sampling Techniques Using Fuzzy Set Theory: A Comprehensive Approach

Year : 2025 | Volume : 12 | Issue : 01 | Page : 29 43
    By

    Ritu Yadav,

  • Pratiksha Tiwari,

  • Sangeeta Malik,

  1. PhD Scholar, Department of Mathematics, Baba Mastnath University (B.M.U), Rohtak, Haryana, India
  2. Assistant Professor, Department of Mangement, Delhi Institute of Advanced Study, Delhi, India
  3. Professors, Department of Mathematics, Baba Mastnath University (B.M.U), Rohtak, Haryana, India

Abstract

Sampling is a critical process in statistics, used to estimate population parameters without needing to examine the entire population. Traditional sampling methods, such as simple random sampling, stratified sampling, and cluster sampling, face limitations when applied to complex or heterogeneous populations with imprecise boundaries. These methods often fail to accurately represent populations with overlapping characteristics or missing data, resulting in sampling bias and reduced accuracy. To address these challenges, this paper proposes an optimized sampling approach that incorporates fuzzy set theory, offering a more flexible and nuanced framework for handling uncertainty and ambiguity in population characteristics. Fuzzy set theory allows for partial membership in multiple categories, making it particularly effective for populations with unclear or overlapping boundaries. This paper presents a fuzzy- based sampling model that defines membership functions for key variables, such as age, income, and health, and applies a fuzzy sampling algorithm to select a sample that better represents the diversity of the population. The model reduces sampling bias by accounting for partial membership across different categories, enhancing both the accuracy and precision of estimations. Comparative analysis demonstrates that the fuzzy sampling model performs better than conventional sampling methods, such as stratified and random sampling, in terms of accuracy, sample variance, and representativeness. The fuzzy model’s ability to accommodate overlapping subgroups and reduce variability makes it particularly beneficial for studies in fields like public health, environmental science, and social research, where populations often span multiple, interconnected categories. Future research directions include expanding the model to handle different types of data structures (e.g., time-series, spatial data) and integrating fuzzy logic with machine learning techniques to optimize sample selection further. Automated tools for designing and calibrating fuzzy membership functions could also make the approach more accessible and practical for real-world applications.

Keywords: Membership functions, fuzzy sampling algorithm, accuracy, precision, statistical modeling

[This article belongs to Research & Reviews: Discrete Mathematical Structures ]

How to cite this article:
Ritu Yadav, Pratiksha Tiwari, Sangeeta Malik. Optimizing Sampling Techniques Using Fuzzy Set Theory: A Comprehensive Approach. Research & Reviews: Discrete Mathematical Structures. 2025; 12(01):29-43.
How to cite this URL:
Ritu Yadav, Pratiksha Tiwari, Sangeeta Malik. Optimizing Sampling Techniques Using Fuzzy Set Theory: A Comprehensive Approach. Research & Reviews: Discrete Mathematical Structures. 2025; 12(01):29-43. Available from: https://journals.stmjournals.com/rrdms/article=2025/view=211540


References

  1. Bellman RE, Zadeh LA. Decision-making in a fuzzy environment. Manage Sci. 1970;17(4):B-141.
  2. Bahl S, Tuteja RK. Ratio and product type exponential estimator. Inf Optim Sci. 1991;12(1):159–63.
  3. Chouhan S. Improved estimation of parameters using auxiliary information in sample surveys [Ph.D. thesis]. Ujjain, India: Vikram University; 2012.
  4. Cochran WG. Sampling Techniques. 3rd ed. New York: Wiley; 1977.
  5. Dubois D, Prade H. Fuzzy Sets and Systems: Theory and Applications. New York: Academic Press; 1980.
  6. Holt D, Smith TMF. Post-stratification. J R Stat Soc Ser A. 1979;142(1):33–46.
  7. Ige AF, Tripathi TP. On double sampling for post-stratification and use of auxiliary information. J Indian Soc Agric Stat. 1987;39:191–201.
  8. Kaufmann A, Gupta MM. Introduction to Fuzzy Arithmetic: Theory and Applications. New York: Van Nostrand Reinhold; 1985.
  9. Kish L. Survey Sampling. New York: Wiley; 1965.
  10. Lone HA, Tailor R. Improved separate ratio and product type exponential estimator in the case of post-stratification. Stat Transit. 2014;16(1):53–64.
  11. Malik S, Tailor R. Modified unbiased estimator using auxiliary variables. AIP Conf Proc. 2022;2597(1).
  12. Murthy MN. Sampling Theory and Methods. Calcutta: Statistical Publishing Society; 1967.
  13. Raj D. The Design of Sample Surveys. New York: McGraw Hill; 1972.
  14. Robson DS. Applications of multivariate polykays to the theory of unbiased radio-type estimation. J Am Stat Assoc. 1957;52:511–22.
  15. Singh MP. Ratio cum product method of estimation. Metrika. 1967;12(1):34–42.
  16. Singh R, Tailor R. Estimation of finite population mean with known coefficient of variation of auxiliary character. Stat Transit. 2003;6(5):865–76.
  17. Stephan F. The expected value and variance of the reciprocal and other negative powers of a positive Bernoullian variate. Ann Math Stat. 1945;16:50–61.
  18. Tailor R, Lone HA. Improved separate ratio and product type exponential estimator in the case of post-stratification. Stat Transit. 2015;16(1):53–64.
  19. Zadeh LA. Fuzzy sets. Inf Control. 1965;8(3):338–53.
  20. Zimmermann HJ. Fuzzy Set Theory—and Its Applications. New York: Springer Science & Business Media; 1996.
  21. Khuat TT, Ruta D, Gabrys B. Hyperbox-based machine learning algorithms: a comprehensive survey. Soft Comput. 2021;25(2):1325–63.
  22. Singh A, Kulkarni H, Smarandache F, Vishwakarma GK. Computation of Separate Ratio and Regression Estimator Under Neutrosophic Stratified Sampling: An Application to Climate Data. J Fuzzy Ext Appl. 2024.
  23. Beer M. Fuzzy probability theory. In: Granular, Fuzzy, and Soft Computing. New York: Springer US; 2023. p. 51–75.
  24. Aslam MU, Xu S, Noor-ul-Amin M, Hussain S, Waqas M. Fuzzy control charts for individual observations to analyze variability in health monitoring processes. Appl Soft Comput. 2024;164:111961.
  25. Smith P, Greenfield S. Towards Refined Autism Screening: A Fuzzy Logic Approach with a Focus on Subtle Diagnostic Challenges. Mathematics. 2024;12(13):2012.
  26. Jiang J, Tang S, Han D, Fu G, Solomatine D, Zheng Y. A comprehensive review on the design and optimization of surface water quality monitoring networks. Environ Model Softw. 2020;132:104792.
  27. Mubarak SMJ, Crampton A, Carter J, Parkinson S. Robust data expansion for optimised modelling using adaptive neuro-fuzzy inference systems. Expert Syst Appl. 2022;189:116138.
  28. Nguyen PH, Fayek AR. Applications of fuzzy hybrid techniques in construction engineering and management research. Autom Constr. 2022;134:104064.
  29. Dellermann D, Lipusch N, Ebel P, Popp KM, Leimeister JM. Finding the unicorn: Predicting early stage startup success through a hybrid intelligence method. arXiv preprint. 2021. arXiv:2105.03360.
  30. Yilin C, Jianhua W. Optimization and Implementation of Fuzzy Logic Controllers for Precise Path Tracking in Autonomous Driving. J Sustain. 2022.
Regular Issue Subscription Original Research
Volume 12
Issue 01
Received 28/03/2025
Accepted 22/04/2025
Published 28/04/2025
Publication Time 31 Days
274

Login


My IP

PlumX Metrics