Abstract
In this paper, we further study the distributivity for uninorms with noncontinuous underlying operators, where the first uninorm is in one of the known classes of uninorms, i.e., Umax, Umin, uninorms continuous in the open unit square and the second uninorm has a noncontinuous underlying operator. When the first uninorm is in Umax or Umin, the necessary conditions (resp. sufficient conditions) for the distributivity for uninorms are discussed with respect to some certain conditions. Considering the first uninorm continuous in the open unit square, the characterizations of the distributivity for uninorms are discussed. In particular, the uninorms in the distributivity equation have to be both disjunctive or both conjunctive at the same time, where the first uninorm is in Umax, Umin and uninorms continuous in the open unit square.
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