On testing hypothesis of fuzzy sample mean

  • Berlin WuEmail author
  • Shu -Kwang Chang


In many expositions of fuzzy methods, fuzzy techniques are described as an alternative to a more traditional statistical approach. In this paper, we present a class of fuzzy statistical decision process in which testing hypothesis can be naturally reformulated in terms of interval-valued statistics. We provide the definitions of fuzzy mean, fuzzy distance as well as investigation of their related properties. We also give some empirical examples to illustrate the techniques and to analyze fuzzy data. Empirical studies show that fuzzy hypothesis testing with soft computing for interval data are more realistic and reasonable in the social science research. Finally certain comments are suggested for the further studies. We hope that this reformation will make the corresponding fuzzy techniques more acceptable to researchers whose only experience is in using traditional statistical methods.

Key words

membership function fuzzy sampling survey fuzzy mean human thought 


  1. [1]
    D. Dubois and H. Prade, Fuzzy sets in approximate reasoning, Part 1: Inference with possibility distributions. Fuzzy Sets and Systems,40 (1991), 143–202.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    J. Goutsias, R.P.S. Mahler and H.T. Nguyen (eds.), Random Sets: Theory and Applications. Springer-Verlag, N.Y., 1997.zbMATHGoogle Scholar
  3. [3]
    G.S. Liang and M.J. Wang, A fuzzy multicriteria decision making method for facility site selection. International Journal of Production Research,29 (1991), 2313–2330.zbMATHCrossRefGoogle Scholar
  4. [4]
    H.T. Nguyen and B. Wu, Fuzzy Mathematics and Statistical Applications. Hua-Tai Book Company, Taipei, 2000.Google Scholar
  5. [5]
    H.T. Nguyen and B. Wu, Fundamentals of Statistics with Fuzzy Data. Springer-Verlag, Heidelberg, 2006.zbMATHGoogle Scholar
  6. [6]
    M. Stojakovic, Fuzzy random variables, expectation, and martingales. Journal of Mathematical Analysis and Applications,184 (1994), 594–606.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    B. Wu and C. Sun, Interval-valued statistics, fuzzy logic, and their use in computational semantics. Journal of Intelligent and Fuzzy Systems,11 (2001), 1–7.Google Scholar
  8. [8]
    B. Wu and W. Yang, Application of fuzzy statistics in the sampling survey. Development and Application for the Quantity Methods of Social Science. Academic Sinica, Taiwan, 1998, 289–316.Google Scholar
  9. [9]
    H.J. Zimmermann, Fuzzy Set Theory and Its Applications, Kluwer Academic, Boston, 1991.zbMATHGoogle Scholar

Copyright information

© JJIAM Publishing Committee 2007

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNational Chengchi UniversityTaiwan
  2. 2.Department of Mathematical SciencesNational Chengchi UniversityTaiwan

Personalised recommendations