Interval-valued intuitionistic fuzzy implications  Construction, properties and representability
Firstly, this work studies the class of representable (co)implications obtained by idempotent aggregations and pair of dual interval functions, namely fuzzy implications and coimplications. Following the same construction, as the main contribution in the context of the interval-valued intuitionistic fuzzy logic, which is conceived by Atanassov, the class of representable Atanassovs intuitionistic fuzzy implications is obtained by composition of idempotent interval aggregations and dual pairs of representable fuzzy implications and coimplications. Additionally, the conditions under which relevant properties of fuzzy implications and Atanassovs intuitionistic fuzzy implications are preserved by such constructions are investigated. Furthermore, taking into account the projection functions and related (interval-valued) Atanassovs intuitionistic fuzzy implications, it also shows that representable (interval-valued) Atanassovs intuitionistic fuzzy implications preserve (degenerate) diagonal elements.
fuzzy connectives and aggregation operator interval-valued fuzzy logic interval-valued intuitionistic implication n-dual operator