A note on the convexity assumption of possibilistic correlation
2012 (English)In: Applied Mathematics Letters, ISSN 0893-9659, E-ISSN 1873-5452, Vol. 25, no 4, 672-675 p.Article in journal (Refereed) Published
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].
Place, publisher, year, edition, pages
2012. Vol. 25, no 4, 672-675 p.
Joint possibility distribution, Possibilistic correlation coefficient
Computer and Information Science
IdentifiersURN: urn:nbn:se:su:diva-76112DOI: 10.1016/j.aml.2011.08.023ISI: 000300809300002OAI: oai:DiVA.org:su-76112DiVA: diva2:526207