A note on the convexity assumption of possibilistic correlation

作者：Majlender Peter^*

来源：Applied Mathematics Letters, 2012, 25(4): 672-675.

DOI：10.1016/j.aml.2011.08.023

• Joint possibility distribution
• Possibilistic correlation coefficient

In 2005, 2005, Carlsson, Fuller and Majlender introduced a measure of possibilistic correlation of fuzzy numbers A and B by their joint possibility distribution C as an average degree of interaction between the gamma-level sets of A and B as compared to their individual dispersions. They proved that this possibilistic correlation coefficient can never exceed 1 in absolute value, if all gamma-level sets of the joint possibility distribution C are convex. %26lt;br%26gt;In this communication, we shall formulate a special class of joint possibility distributions with non-convex gamma-level sets, for which the correlation coefficient can take values outside the interval [-1, 1]. in particular, this result will show that the assumption about the convexity of the level sets of C is essential for the possibilistic correlation to be bounded by the interval [-1, 1].

• 出版日期2012-4