Intuitionistic Fuzzy Linguistic Quantifiers Based on Intuitionistic Fuzzy-Valued Fuzzy Measures and integrals

In this paper, we generalize Ying’s model of linguistic quantifiers [M.S. Ying, Linguistic quantifiers modeled by Sugeno integrals, Artificial Intelligence, 170 (2006) 581-606] to intuitionistic linguistic quantifiers. An intuitionistic linguistic quantifier is represented by a family of intuitionistic fuzzy-valued fuzzy measures and the intuitionistic truth value (the degrees of satisfaction and non-satisfaction) of a quantified proposition is calculated by using intuitionistic fuzzy-valued fuzzy integral. Description of a quantifier by intuitionistic fuzzy-valued fuzzy measures allows us to take into account differences in understanding the meaning of the quantifier by different persons. If the intuitionistic fuzzy linguistic quantifiers are taken to be linguistic fuzzy quantifiers, then our model reduces to Ying’s model. Some excellent logical properties of intuitionistic linguistic quantifiers are obtained including a prenex norm form theorem. A simple example is presented to illustrate the use of intuitionistic linguistic quantifiers.