Differently implicational hierarchical inference algorithm under interval-valued fuzzy environment

Under interval-valued fuzzy environment, based on the differently implicational idea and hierarchical inference mechanism, the interval-valued universal triple I algorithm is put forward. To begin with, the interval-valued fuzzy implications and related residual pairs are researched. Furthermore, the interval-valued universal triple I principles are proposed, and the optimal solutions of the interval-valued universal triple I algorithm are achieved from the viewpoints of residual pairs together with the R-implications, and the corresponding hierarchical inference mode is established, meanwhile the reversible properties of the interval-valued universal triple I algorithm are proved. Finally, it is verified by examples that the interval-valued universal triple I algorithm performs better than the interval-valued triple I algorithm.