On uninorms and nullnorms on direct product of bounded lattices
Martin Kalina · Open Physics · 2016
Abstract We will study uninorms on the unit square endowed with the natural partial order defined coordinate-wise. We will show that we can choose arbitrary pairs of incomparable elements, (a, e) and construct a uninorm whose neutral element is e and annihilator is a. As a special case we construct uninorms which are at the same time also nullnorms (or, expressed another way, we construct proper nullnorms with neutral element). We will also generalize this result to the direct product of two bounded lattices. I.e., we will show that it is possible to construct nullnorms with a neutral element on the direct product of two bounded lattices.