Fuzzy measures for correlation coefficient of fuzzy numbers

Authors:
Shiang-Tai Liu;Chiang Kao
Affiliations:
Department of Industrial Management, Van Nung Institute of Technology, Chung-Li, Taiwan 320, ROC;Department of Industrial Management, National Cheng Kung University, Tainan, Taiwan 70101, ROC
Venue:
Fuzzy Sets and Systems
Year:
2002

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Abstract

Correlation coefficient of random variables has wide applications in statistical analysis. This paper extends the applications to fuzzy environment, with a methodology for calculating the correlation coefficient of fuzzy numbers developed. Different from previous studies, the correlation coefficient calculated in this paper is a fuzzy number, rather than a crisp value. The idea is based on Zadeh's extension principle. A pair of nonlinear programs is formulated to find the α-cut of the fuzzy correlation coefficient. From different values of α, the membership function of the fuzzy correlation coefficient is constructed. To illustrate how to interpret the fuzzy correlation coefficient in real world applications, the correlation between the technology level and management achievement from a sample of 15 machinery firms in Taiwan is exemplified. All indications show that the correlation between technology and management in Taiwan machinery firms is rather low.