Compatibility and representation of observables on type I, II, III fuzzy quantum posets

Gianpiero Cattaneo, Roberto Giuntini, Sylvia Pulmannová

Anatolij Dvurečenskij, Ferdinand Chovanec

Lê Bá Long

We give a representation of an observable on a fuzzy quantum poset of type II by a pointwise defined real-valued function. This method is inspired by that of Kolesárová [6] and Mesiar [7], and our results extend representations given by the author and Dvurečenskij [4]. Moreover, we show that in this model, the converse representation fails, in general.

Anatolij Dvurečenskij

ANATOLU DVUREĆENSKIJ, Beloslav Riečan

We present some models of quantum mechanics which use fuzzy set approaches: fuzzy measurable spaces and fuzzy quantum posets of two types. Also presented are compatibility problems, observables and their representations, functional calculus of observables, and states (= probability measures).

Jarosław Pykacz