Interval-valued Atanassov intuitionistic t-norms and t-conorms endowed with the usual or admissible orders

The interval-valued fuzzy sets and Atanassov intuitionistic fuzzy sets can be extended to a more general framework to simultaneously deal with uncertainty in both membership and non-membership values. This fact leads to the concept of interval-valued Atanassov intuitionistic fuzzy sets (IVAIFS), as given by Atanassov and Gargov (Fuzzy Sets Syst, 31(3):343-349, 1989). In this paper, we focus on the study of interval-valued Atanassov intuitionistic t-norms and t-conorms, studying important properties and characterizations of some of their sub-classes. In addition, we do not only consider just the usual order on IVAIFS, but also admissible orders. Finally, we establish the basis for the use of this study in the approximate reasoning context.

Automated summary

This paper focuses on the study of interval-valued Atanassov intuitionistic t-norms and t-conorms, examining important properties and characterizations of certain sub-classes. The paper also considers admissible orders in addition to the usual order on IVAIFS. Furthermore, the paper establishes the foundation for the use of this study in the context of approximate reasoning.