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Centroid sets with largest weight in Munn semirings for data mining applications

Abawajy, Jemal, Kelarev, Andrei and Zeleznikow, John (2013) Centroid sets with largest weight in Munn semirings for data mining applications. Semigroup Forum, 86 (2). ISSN 0037-1912 (Print) 1432-2137 (Online)

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Abstract

Our main results show that Munn semirings over idempotent semifields possess more convenient properties than the Munn rings over fields. First, we describe all centroid sets that can be generated as ideals of the largest weight in Munn semirings over idempotent semifields. Second, we handle the more general case of all onesided ideals too. The multiplication in the Munn semirings is not commutative and the family of arbitrary one-sided ideals is larger than that of two-sided ideals. It is essential to consider all ideals not only in order to develop theoretical foundations, but also since the larger set of ideals may lead to design of classification and clustering systems with better properties. Our main theorem describes all ideals and one-sided ideals with the largest weight in Munn semirings over idempotent semifields.

Item Type: Article
Uncontrolled Keywords: algebra, mathematics, classification system, Munn semiring, classifier, clusterer, Rees matrix semigroup
Subjects: FOR Classification > 0101 Pure Mathematics
FOR Classification > 0806 Information Systems
Faculty/School/Research Centre/Department > College of Business
Funders: http://purl.org/au-research/grants/arc/DP0880501
Depositing User: VUIR
Date Deposited: 22 Oct 2013 04:53
Last Modified: 10 Jul 2014 23:21
URI: http://vuir.vu.edu.au/id/eprint/22294
DOI: https://doi.org/10.1007/s00233-013-9488-5
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Citations in Scopus: 2 - View on Scopus

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