Index, expressions and properties of interval-valued intuitionistic fuzzy implications - Bedregal, Benjamin Callejas; Visintin, Lidiane; Reiser, Reiser Hax Sander (Trends in Computational and Applied Mathematics, 2013)
<!--StartFragment-->The interval-valued intuitionistic fuzzy logic, an extension of fuzzy logic introduced by Atanassov, integrates the concepts of intuitionistic fuzzy logic and interval-valued fuzzy logic. The former, reflects the measure of vagueness and uncertainty in the diameter of an interval. The latter also considers the hesitation related to the dual construction. This paper considers an expression to interval-valued intuitionistic fuzzy implications, which can be generated by interval-valued aggregation functions acting on mutual-dual pair of 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.