In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on L from the t-norm on a subinterval of L need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other construction methods in the literature are presented.
In this paper, two construction methods have been proposed for uni-nullnorms on any bounded lattices. The difference between these two construction methods and the difference from the existing construction methods have been demonstrated and supported by an example. Moreover, the relationship between our construction methods and the existing construction methods for uninorms and nullnorms on bounded lattices are investigated. The charactertics of null-uninorms on bounded lattice L are given and a contruction method is presented.