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 Atanassov’s 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 Atanassov’s intuitionistic fuzzy implications are preserved by such constructions are investigated. Furthermore, taking into account the projection functions and related (interval-valued) Atanassov’s intuitionistic fuzzy implications, it also shows that representable (interval-valued) Atanassov’s intuitionistic fuzzy implications preserve (degenerate) diagonal elements.