A Study of GD′- Implications, a New Hyper Class of Fuzzy Implications

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