The Idempotency of Convolution Operations on Fuzzy Truth Values

Recently, convolution operations on fuzzy truth values (FTVs, that is, functions from [0, 1] to [0, 1]) and their basic properties have become a hot research area, such as type-2 t-norms, type-2 aggregation operations, type-2 implications, etc., and the closure, monotonicity, distributivity, etc. However, the idempotency of convolution operations has not been studied so far. In this article, we give the equivalent characterization of the idempotency of convolution operations on FTVs.