Remarks on Sugeno Integrals on Bounded Lattices

A discrete Sugeno integral on a bounded distributive lattice L is defined as an idempotent weighted polynomial. Another possibility for axiomatization of integrals to consider compatible aggregation functions, uniquely extending the L-valued fuzzy measures. This paper aims study mentioned unique extension property concerning possible non-distributive lattices. We show that this equivalent distributivity underlying lattice. As byproduct, alternative proof Iseki’s result, stating having prime ideal separation every pair distinct elements distributive, provided.