In this paper, we introduce and study the GD0-operations, which are a hyper class of the known D0-operations. GD0-operations are in fact D0-operations, that are generated not only from the same fuzzy negation. Similar with D0-operations, they are not always fuzzy implications. Nevertheless, some sufficient, but not necessary conditions for a GD0-operation to be a fuzzy implication, will be proved. A study for the satisfaction, or the violation of the basic properties of fuzzy implications, such as the left neutrality property, the exchange principle, the identity principle and the ordering property will also be made. This study also completes the study of the basic properties of D0-implications. At the end, surprisingly an unexpected new result for the connection of the QL-operations and D-operations will be presented.
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