Abstract
We introduce the sum of two n-dimensional observables on a \(\sigma \)-complete MV-effect algebra and on a lexicographic MV-effect algebra, respectively. The sum is based upon a one-to-one correspondence between n-dimensional observables and n-dimensional spectral resolutions. Therefore, the sum of two observables is defined by their n-dimensional spectral resolutions. In addition, we study also the Olson order between n-dimensional observables using the one-to-one correspondence which enables us to show some semigroup properties of the set of n-dimensional observables with respect to the sum and the Olson order.
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The author is very indebted to an anonymous referee for his/her valuable comments and suggestions which improved readability of the paper.
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This study was supported by the Slovak Research and Development Agency under contract APVV-16-0073 and the Grant VEGA No. 2/0142/20 SAV.
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The paper was supported by the grant of the Slovak Research and Development Agency under contract APVV-16-0073 and the Grant VEGA No. 2/0142/20 SAV.
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Dvurečenskij, A. Sum of n-dimensional observables on MV-effect algebras. Soft Comput 25, 8073–8084 (2021). https://doi.org/10.1007/s00500-021-05911-1
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DOI: https://doi.org/10.1007/s00500-021-05911-1