Abstract
A fuzzy system is introduced as a couple ( E , S ) consisting of a σ -orthocomplete effect algebra E and an order-determining set S of σ -additive states on E, which represents a physical system also taking into account the unsharp quantum measurements. Hidden variables and quasi-hidden variables for fuzzy systems are defined in terms of embedding the system into a fuzzy system based on a tribe of fuzzy sets and a fuzzy system based on a σ -MV algebra, respectively. Relations to the existence of a sufficient supply of σ -additive, resp. finitely additive prime states (which generalize the notion of dispersion-free states) are shown. Some Bell-type inequalities are defined and their relations to hidden variables are shown. Some examples are discussed.
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