Advertisement

Correlation Evaluation with Fuzzy Data and its Application in the Management Science

  • Berlin WuEmail author
  • Wei-Shun Sha
  • Juei-Chao Chen
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 583)

Abstract

How to evaluate an appropriate correlation with fuzzy data is an important topic in the educational and psychological measurement. Especially when the data illustrate uncertain, inconsistent and incomplete type, fuzzy statistical method has some promising features that help resolving the unclear thinking in human logic and recognition. Traditionally, we use Pearson’s Correlation Coefficient to measure the correlation between data with real value. However, when the data are composed of fuzzy numbers, it is not feasible to use such a traditional approach to determine the fuzzy correlation coefficient. This study proposes the calculation of fuzzy correlation with three types of fuzzy data: interval, triangular and trapezoidal. Empirical studies are used to illustrate the application for evaluating fuzzy correlations. More related practical phenomena can be explained by this appropriate definition of fuzzy correlation.

Keywords

Membership Function Fuzzy Number Fuzzy Measure Fuzzy Data Fuzzy Time Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1999)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Dubois, D., Prade, H.: Fuzzy sets in approximate reasoning, part 1: inference with possibility distributions. Fuzzy Sets Syst. 40, 143–202 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Lowen, R.: A fuzzy language interpolation theorem. Fuzzy Sets Syst. 34, 33–38 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Ruspini, E.: Approximate reasoning: past, present, future. Inf. Sci. 57, 297–317 (1991)CrossRefGoogle Scholar
  5. 5.
    Wu, B., Hsu, Y.: The use of Kernel set and sample memberships in the identification of nonlinear time series. Soft Comput. 8(3), 207–216 (2002)CrossRefGoogle Scholar
  6. 6.
    Bustince, H., Burillo, P.: Correlation of interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 74, 237–244 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Hong, D.: Fuzzy measures for a correlation coefficient of fuzzy numbers under \(T_w\)—(the weakest t-norm)-based fuzzy arithmetic operations. Fuzzy Sets Syst. 176, 150–160 (2006)zbMATHGoogle Scholar
  8. 8.
    Liu, S., Kao, C.: Fuzzy measures for correlation coefficient of fuzzy numbers. Fuzzy Sets Syst. 128, 267–275 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Yu, C.: Correlation of fuzzy numbers. Fuzzy Sets Syst. 55, 303–307 (1993)CrossRefzbMATHGoogle Scholar
  10. 10.
    Hong, D., Hwang, S.: Correlation of intuitionistic fuzzy sets in probability space. Fuzzy Sets Syst. 75, 77–81 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Wang, G., Li, X.: Correlation and information energy of interval-valued fuzzy numbers. Fuzzy Sets Syst. 103, 169–175 (1999)CrossRefzbMATHGoogle Scholar
  12. 12.
    Chiang, D.A., Lin, N.P.: Correlation of fuzzy sets. Fuzzy Sets Syst. 102, 221–226 (1999)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNational Cheng Chi UniversityTaipeiTaiwan
  2. 2.Graduate Institute of Business AdministrationFu Jen Catholic UniversityNew TaipeiTaiwan
  3. 3.Department of Statistics and Information ScienceFu Jen Catholic UniversityNew TaipeiTaiwan

Personalised recommendations