Fuzzy Sets and Fuzzy Relational Structures as Chu Spaces

Chu spaces, which derive from the Chu construct of ∗-autonomous categories, can be used to represent most mathematical structures. Moreover, the logic of Chu spaces is linear logic. Most efforts to incorporate fuzzy set theory into the realm of linear logic are based on the assumption that fuzzy and linear negation are identical operations. We propose an incorporation based on the opposite assumption and we provide an interpretation of some linear connectives. Furthermore, we show that it is possible to represent any fuzzy relational structure as a Chu space by means of the functor G.