On fuzzy hidden variables (Q2565804)

Fuzzy system is a couple \((E,S)\) consisting of a \(\sigma\)-orthocomplete effect algebra \(E\) and an order determining set \(S\) of \(\sigma\)-additive states on \(E\). Hidden variables (quasi-hidden variables, respectively) are defined in terms of embedding the system into a fuzzy system based on a tribe of fuzzy sets (based on a \(\sigma\)-MV algebra, respectively). Characterization of fuzzy systems admitting hidden variables (quasi-hidden variables, respectively) by means of a generating family of \(\sigma\)-additive (finitely additive, respectively) prime states is given. Bell-type inequalities are defined and their relations to hidden variables are shown.