Fuzzy integrals and linearity Original Research Article

Linearity and generalized linearity of fuzzy integrals are studied. For continuous from below fuzzy integrals, linearity leads to the Lebesgue integral while the comonotone linearity results to the Choquet integral with respect to a selfdual fuzzy measure m. Similar results in the case of idempotent linearity are presented. Some open problems were stated, too. Finally, pseudo-linearity related to two types of semirings is discussed.