We show that under some natural conditions, we are able to lift an n-dimensional spectral resolution from one monotone \(\sigma \)-complete unital po-group into another one, when the first one is a \(\sigma \)-homomorphic image of the second one. We note that an n-dimensional spectral resolution is a mapping from \(\mathbb R^n\) into a quantum structure which is monotone, left-continuous with non-negative increments and which is going to 0 if one variable goes to \(-\infty \) and it goes to 1 if all variables go to \(+\infty \). Applying this result to some important classes of effect algebras including also MV-algebras, we show that there is a one-to-one correspondence between n-dimensional spectral resolutions and n-dimensional observables on these effect algebras which are a kind of \(\sigma \)-homomorphisms from the Borel \(\sigma \)-algebra of \({\mathbb {R}}^n\) into the quantum structure. An important used tool are two forms of the Loomis–Sikorski theorem which use two kinds of tribes of fuzzy sets. In addition, we show that we can define three different kinds of n-dimensional joint observables of n one-dimensional observables.

我们表明，在某些自然条件下，当第一个是\（\ sigma \）时，我们能够将n维光谱分辨率从一个单调\（\ sigma \）-完全单位po-group提升到另一个。 -第二个图像的同态图像。我们注意到，n维光谱分辨率是从\（\ mathbb R ^ n \）到量子结构的映射，该结构是单调的，以非负增量向左连续，并且如果一个变量到达\，它将变为0 。 （-\ infty \），如果所有变量都转到\（+ \ infty \），则该值为1。将这一结果应用于一些重要的效应代数，包括MV代数，我们证明在这些效应代数上，n维光谱分辨率和n维可观量之间存在一一对应的关系，这是\（ \ sigma \） -从\（{\ mathbb {R}} ^ n \）的Borel \（\ sigma \）-代数的同态到量子结构。一种重要的使用工具是Loomis-Sikorski定理的两种形式，它们使用两种模糊集部落。此外，我们表明可以定义n个一维可观测量的三种不同类型的n维联合可观测量。