Modal fuzzy quantities and applications to control

In this paper modal fuzzy quantities and an arithmetic to operate with them are introduced. Based on the identification of a fuzzy quantity with the set of predicates it accepts and rejects, a modal fuzzy quantity is defined. Modal fuzzy intervals arise as a particular case, with either existential or universal modal intervals as alpha-cuts. Modal interval analysis can then be applied to the alpha-cuts, deriving a modal fuzzy arithmetic and new semantic theorems. These ones will allow to cast a suitable interpretation to existential and universal expressions involving fuzzy intervals, by requiring a non-fuzzy semantics to hold for each cut. A particular application of these ideas in the context of control theory is discussed.