Left (right) semi-uninorms and coimplications on a complete lattice

摘要

In this paper, we firstly discuss the deresidual operations of left (right) semi-uninorms and show which properties they satisfy. Then, we investigate the left and right semi-uninorms induced by a coimplication and give some conditions such that the operations induced by a coimplication constitute left or right semi-uninorms. Finally, we demonstrate that the meet-semilattice of all disjunctive right (left) boolean AND-distributive left (right) semi-uninorms is order-reversing isomorphic to the join-semilattice of all right boolean OR-distributive coimplications, which satisfy the neutrality principle. (C) 2015 Elsevier B.V. All rights reserved.