Abstract
This article introduces Munn semirings, which generalize the well known concept of the Munn rings. Our main theorem strengthens previous results by describing all centroid sets for classification and clustering systems that can be generated as ideals with the largest weight in Munn semirings over idempotent semifields. A description of centroid sets that can be generated as one-sided ideals with the largest weight among all one-sided ideals in Munn semirings over idempotent semifields is obtained too.
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Acknowledgements
The first author was supported by Discovery grant DP0880501 from Australian Research Council. The second author was supported by ARC Discovery grant DP0449469.
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Communicated by Mikhail Volkov.
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Abawajy, J., Kelarev, A.V. & Zeleznikow, J. Centroid sets with largest weight in Munn semirings for data mining applications. Semigroup Forum 87, 617–626 (2013). https://doi.org/10.1007/s00233-013-9488-5
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DOI: https://doi.org/10.1007/s00233-013-9488-5