A note on the convexity assumption of possibilistic correlation

• 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. 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].

Ämnesord

NATURVETENSKAP  -- Matematik -- Annan matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Other Mathematics (hsv//eng)

NATURVETENSKAP  -- Data- och informationsvetenskap -- Annan data- och informationsvetenskap (hsv//swe)

NATURAL SCIENCES  -- Computer and Information Sciences -- Other Computer and Information Science (hsv//eng)

Nyckelord

Joint possibility distribution

Possibilistic correlation coefficient

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