Intuitionistic fuzzy Choquet integrals and their application in modeling linguistic quantifiers

The notion of intuitionistic fuzzy Choquet integrals is introduced. Then, some nice properties, including component-wise decomposition property, duality property, a simple form of the discrete expression, of intuitionistic fuzzy Choquet integrals are studied. As an application of intuitionistic fuzzy Choquet integrals, Cui and Li´s model (L.C.Cui, Y.M.Li, Linguistic quantifiers based on Choquet integrals, International Journal of Approximate Reasoning, 48 (2008) 559-582.) of linguistic quantifiers is generalized to intuitionistic linguistic quantifiers. Description of a quantifier by intuitionistic fuzzy measures allows us to take into account differences in understanding the meaning of the quantifier by different persons. Some elegant logical properties of linguistic quantifiers are derived within this approach.