Correlation of fuzzy numbers by α-cut method

Authors:
Wen-Liang Hung;Jong-Wuu Wu
Affiliations:
Department of Mathematics Education, National Hsinchu Teachers College, Hsin-Chu, Taiwan, R.O.C.;Department of Statistics, Tamkang University, Tamsui, Taipei, Taiwan, R.O.C.
Venue:
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Year:
2002

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Abstract

In this paper, we propose a method to calculate the correlation coefficient of fuzzy numbers by means of "α-cut". This value obtained from our formula tells us not only the strength of relationship between the fuzzy numbers, but also whether the fuzzy numbers are positively or negatively related. This approach looks better than previous methods which only evaluate the strength of the relation. Furthermore, we extend the "α-cut" method to interval-valued fuzzy numbers. The value of the correlation coefficient between interval-valued fuzzy numbers lies in the interval [-1, 1], as computed from our formula.