Distributivity for Semi-Nullnorms Over 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. In this paper, we continue to investigate the same topic as the above by focusing on semi-nullnorms and semi-t-operators, which are generalization of nullnorms and t-operators by omitting commutativity and associativity, and commutativity, respectively. The obtained results are not only the full characterization of this kind of distributivity equation, but also extensions of distributivity for nullnorms and for semi-nullnorms. Moreover, this paper finishes the full characterization of distributivity between semi-nullnorms and semi-t-operators together with Refs. 6 and 20. [ABSTRACT FROM AUTHOR]