The interval-valued intuitionistic fuzzy logic, an extension of fuzzy logic, integrates the concepts of interval-valued fuzzy logic and intuitionistic fuzzy logic. The former, reflects the measure of vagueness and uncertainty in the diameter of an interval. The latter considers the hesitation related to the dual construction. This paper considers an expression to interval-valued intuitionistic fuzzy implications, which can be generated by idempotent interval-valued aggregation functions acting on a pair of mutual-dual functions, an interval-valued implication and its corresponding coimplication. Then, we show under which conditions interval-valued intuitionistic fuzzy implications are diagonal preserving operators. We study not only properties of such operators which were extended to intuitionistic fuzzy logic, but also analyse properties truly intuitionistic. The canonical representation in the class of such operators and an interval version of an intuitionistic fuzzy index conclude this study.
interval-valued intuitionistic fuzzy connectives; interval-valued intuitionistic fuzzy implication; intuitionistic index
