INFORMATION SCIENCES, vol.298, pp.22-35, 2015 (SCI-Expanded)
We present some relations between an external direct product and an internal direct product of a family of integral V-distributive binary aggregation functions. Relations between a direct decomposition of the unit and a family of pairwise comaximal elements in a lattice with an integral V-distributive binary aggregation function are investigated. Using these results, the classification of all integral V-distributive binary aggregation functions on a lattice of length 3 and a description of all lattices of length 3 with an integral V-distributive binary aggregation function are given. (C) 2014 Elsevier Inc. All rights reserved.