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

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