On the Lower Limit for Possibilistic Correlation Coefficient with Identical Marginal Possibility Distributions

Abstract

In 2011 Fuller et al. [An improved index of interactivity for fuzzy numbers, Fuzzy Sets and Systems, 165 (2011), pp. 50–60] introduced a new measure of interactivity between fuzzy numbers (interpreted as possibility distributions), called the weighted possibilistic correlation coefficient, which can be determined from their joint possibility distribution. They also left two questions open regarding the lower limit of the weighted possibilistic correlation coefficient of marginal possibility distribution with the same membership function. In this paper we will answer these questions not only in the case of fuzzy numbers, but also for quasi fuzzy numbers.