Idempotent uninorms and nullnorms on bounded posets

Document Type : Research Paper


Department of Mathematics, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia


The paper deals with uninorms and nullnorms as basic semi-group  operations which are commutative and monotone (increasing). These operations were first introduced on the unit interval and later generalized to bounded lattices. In [Kalina 2019], they were introduced on bounded posets. This contribution is a generalization and extension of the results in [Kalina 2019]. Some necessary and some sufficient conditions for the existence of idempotent uninorms and idempotent nullnorms  on bounded posets are studied. Finally, some application examples are provided.