Novel Construction of Copulas Based on ($\alpha ,\beta$) Transformation for Fuzzy Random Variables

Abstract

The paper introduces a method for the construction of bivariate copulas with the usage of specific values of the parameters α and β ( α , β transformation) and the parameters κ and λ in their domain. The produced bivariate copulas are defined in four subrectangles of the unit square. The bounds of the produced copulas are investigated, while a novel construction method for fuzzy copulas is introduced, with the usage of the produced copulas via α , β transformation in four subrectangles of the unit square. Following this construction procedure, the production of an infinite number of copulas and fuzzy copulas could be possibly achieved. Some applications of the proposed methods are presented.