On the characterization of distributivity equations about quasi-arithmetic means (Q291277)

The authors do some investigations about distributivity equations between quasi-arithmetic means and some binary operators such as nullnorms, semi-nullnorms and semi-\(t\)-operators. After recalling the definitions of these operators, they first show that the distributivity equations between nullnorms and quasi-arithmetic means degenerate into the distributivity equations between \(t\)-norms or \(t\)-conorms and quasi-arithmetic-means. Then, the authors show that there are new solutions for the semi-\(t\)-operators distributive over quasi-arithmetic means. These new solutions extend the previous one about the distributivity between \(t\)-norms and quasi-arithmetic means.