In this paper, we develop a novel computation model of Intuitionistic Fuzzy Values with the usage of fuzzy negations and Archimedean copulas. This novel computation model’s structure is based on the extension of the existing operations of intuitionistic fuzzy values with some classes of fuzzy negations. Many properties of the proposed operations are investigated and proved. Additionally, in this paper we introduce the concepts of intuitionistic fuzzy Archimedean copula weighted arithmetic and geometric aggregation operators based on fuzzy negations, including a further analysis of their properties. Finally, using a case study from an already published paper we found that our method has many advantages.

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.