The Left And Right Distributivity Between Semi-t-operators

The problem of distributivity was posed many years ago and it has been investigated for families of certain operations,such as t-norms,t-conorms,uninorms and nullnorms.As a kind of important fuzzy operator in fuzzy mathematics,t-norm has widely used in fuzzy logic,fuzzy control,information aggregation theory and some artificial intelligence theories.Semi-t-operator is a type of T-norms and S-norms,which has an important role in the field of fuzzy mathematics.So in this paper,we will investigate the same topic as the above by focusing on semi-t-operators,which are generalization of t-operators by omitting commutativity.To solve these problems,the main work of this paper is as follows:First,we introduce some basic concepts about t-norms,t-conorms,nullnorms and semi-t-operators in detail.Second,we introduce new concepts about quasi-t-operator and the distri-bution equation which is useful in the last paper.At last,we make a deep research about the distribution between semi-t-operators comprehensively,and give their structure charts depending on their properties.In fact,this is also the future work recommended by Drygas in Ref.[13].Our results are not only the full characterization of this distributivity,but also extension of the previous ones about distributivity for semi-nullnorms and between semi-t-operators and semi-nullnorms.